Papers - Computational Physics @ GT

Archival Publications

2026

Radhakrishnan, A., Wilfong, B., Bryngelson, S. H., & Schäfer, F. (2026). Shocks without shock capturing: Information geometric regularization of finite volume methods for Navier-Stokes-like problems. arXiv:2604.06546.

@unpublished{Radhakrishnan26,
  author = {Radhakrishnan, A. and Wilfong, B. and Bryngelson, S. H. and Schäfer, F.},
  title = {Shocks without shock capturing: Information geometric regularization of finite volume methods for {N}avier-{S}tokes-like problems},
  note = {arXiv:2604.06546},
  file = {radhakrishnan-arxiv-26.pdf},
  arxiv = {arXiv.2604.06546},
  year = {2026},
  doi = {10.48550/arXiv.2604.06546}
}

Shock waves in high-speed fluid dynamics produce near-discontinuities in the fluid momentum, density, and energy. Most contemporary works use artificial viscosity or limiters as numerical mitigation of the Gibbs–Runge oscillations that result from traditional numerics. These approaches face a delicate balance in achieving sufficiently regular solutions without dissipating fine-scale features, such as turbulence or acoustics. Recent work by Cao and Schäfer introduces information geometric regularization (IGR), the first inviscid regularization method for fluid dynamics. IGR replaces shock singularities with smooth profiles of adjustable width, without dissipating fine-scale features. This work provides a strategy for the practical use of IGR in finite-volume-based numerical methods. We illustrate its performance on canonical test problems and compare it against established approaches based on limiters and Riemann solvers. Results show that the finite volume IGR approach recovers the expected solutions in all cases. Across canonical benchmarks, IGR achieves accuracy competitive with WENO and LAD shock-capturing schemes in both smooth and discontinuous flow regimes. The IGR approach is computationally light, with meaningfully fewer memory accesses and arithmetic operations per time step.

Goldstein, B. I., Ramsey, D. N., Yu, H., Bryngelson, S. H., & Ahuja, K. K. (2026). Performance of Sharply Bent Acoustic Resonators at High Sound Levels. AIAA Journal.

@article{goldstein26,
  author = {Goldstein, Bailey I. and Ramsey, David N. and Yu, Haocheng and Bryngelson, Spencer H. and Ahuja, K. K.},
  title = {Performance of Sharply Bent Acoustic Resonators at High Sound Levels},
  journal = {AIAA Journal},
  file = {goldstein-AIAAJ-26.pdf},
  year = {2026},
  doi = {10.2514/1.J066497}
}

This study examines the effect of a single, sharp 90 deg bend placed along the length of a quarter-wave resonator (QWR) on its sound absorption. 3D-printed QWRs were tested in a two-microphone impedance tube both with low-level, broadband noise (less than 100 dB re 20 uPa) and high-amplitude, discrete tones ranging from incident sound pressure levels of 120 to 148 dB re 20 uPa. At low sound levels (and herein, broadband noise), the QWR resonance frequencies and absorption coefficients depended only subtly on the location of the bend, changing a maximum of approximately 4 and 2%, respectively, relative to the lowest value. For high-amplitude discrete tones, at 134 dB and higher, the QWRs exhibited meaningful nonlinearities that depended on the bend location. Direct numerical simulations of two-dimensional model problems are presented, linking experimentally observed trends to acoustically induced vortex formation in the QWR interior.

Vaca-Revelo, D., Wilfong, B., Bryngelson, S. H., & Gnanaskandan, A. (2026). Hardware-Accelerated Phase-Averaging for Cavitating Bubbly Flows. International Journal of Multiphase Flow, 199, 105674.

@article{Vaca26,
  author = {Vaca-Revelo, D. and Wilfong, B. and Bryngelson, S. H. and Gnanaskandan, A.},
  title = {Hardware-Accelerated Phase-Averaging for Cavitating Bubbly Flows},
  journal = {International Journal of Multiphase Flow},
  file = {vaca-IJMF-26.pdf},
  year = {2026},
  pages = {105674},
  volume = {199},
  doi = {10.1016/j.ijmultiphaseflow.2026.105674}
}

We present a comprehensive validation, performance characterization, and scalability analysis of a hardware-accelerated phase-averaged multiscale solver designed to simulate acoustically driven dilute bubbly suspensions. The carrier fluid is modeled using the compressible Navier-Stokes equations. The dispersed phase is represented through two distinct subgrid formulations: a volume-averaged model that explicitly treats discrete bubbles within a Lagrangian framework, and an ensemble-averaged model that statistically represents the bubble population through a discretized distribution of bubble sizes. For both models, the bubble dynamics are modeled via the Keller–Miksis equation. For the GPU cases, we use OpenACC directives to offload computation to the GPUs. The volume-averaged model is validated against the analytical Keller-Miksis solution and experimental measurements, showing excellent agreement with root-mean-squared errors of less than 8% for both single-bubble oscillation and collapse scenarios. The ensemble-averaged model is validated by comparing it to volume-averaged simulations. On an NCSA Delta node with 4 NVIDIA A100 GPUs, we observe a speedup 16-fold compared to a 64-core AMD Milan CPU. The ensemble-averaged model offers additional reductions in computational cost by solving a single set of averaged equations, rather than multiple stochastic realizations. However, the volume-averaged model enables the interrogation of individual bubble dynamics, rather than the averaged statistics of the bubble dynamics. Weak and strong scaling tests demonstrate good scalability across both CPU and GPU platforms. These results show the proposed method is robust, accurate, and efficient for the multiscale simulation of acoustically driven dilute bubbly flows.

Sanchez, V., Remillard, S., Abeid, B. A., Bu, L., Bryngelson, S. H., Yang, J., Estrada, J. B., & Rodriguez Jr., M. (2026). Hierarchical Bayesian constitutive model selection for high-strain-rate soft material characterization. Soft Matter.

@article{Sanchez26,
  author = {Sanchez, Victor and Remillard, Sawyer and Abeid, Bachir A. and Bu, Lehu and Bryngelson, Spencer H. and Yang, Jin and Estrada, Jonathan B. and {Rodriguez Jr.}, Mauro},
  title = {Hierarchical {B}ayesian constitutive model selection for high-strain-rate soft material characterization},
  journal = {Soft Matter},
  file = {sanchez-soft-26.pdf},
  year = {2026},
  doi = {10.1039/D5SM01193K}
}

The high-fidelity characterization of soft, tissue-like materials under ultra-high-strain-rate conditions is critical in engineering and medicine. Still, it remains challenging due to limited optical access, sensitivity to initial conditions, and experimental variability. Microcavitation techniques (e.g., laser-induced microcavitation) have emerged as a viable method for determining the mechanical properties of soft materials in the ultra-high-strain-rate regime (higher than 10^3 1/s); however, they are limited by measurement noise and uncertainty in parameter estimation. A hierarchical Bayesian model selection method is employed using the Inertial Microcavitation Rheometry (IMR) technique to address these limitations. With this method, the parameter space of different constitutive models is explored to determine the most credible constitutive model that describes laser-induced microcavitation bubble oscillations in soft, viscoelastic, transparent hydrogels. The target data/evidence is computed using a weighted Gaussian likelihood with a hierarchical noise scale, which enables the quantification of uncertainty in model plausibility. Physically informed priors, including range-invariant, stress-based parameter priors, a model-redundancy prior, and a Bayesian Information Criterion motivated model prior, penalize complex models to enforce Occam’s razor. Using a precomputed grid of simulations, the probabilistic model selection process enables an initial guess for the Maximum A Posteriori (MAP) material parameter values. Synthetic tests recover the ground-truth models and expected parameters. Using experimental data for gelatin, fibrin, polyacrylamide, and agarose, MAP simulations of credible models reproduce the data. Moreover, a cross-institutional comparison of 10% gelatin indicates consistent constitutive model selection.

Wilfong, B., Le Berre, H., Radhakrishnan, A., Gupta, A., Vickers, D. J., Vaca-Revelo, D., Adam, D., Yu, H., Lee, H., Chreim, J. R., Carcana Barbosa, M., Zhang, Y., Cisneros-Garibay, E., Gnanaskandan, A., Rodriguez Jr., M., Budiardja, R. D., Abbott, S., Colonius, T., & Bryngelson, S. H. (2026). MFC 5.0: An exascale many-physics flow solver. Computer Physics Communications, 322, 110055.

@article{Wilfong26,
  author = {Wilfong, Benjamin and {Le Berre}, Henry and Radhakrishnan, Anand and Gupta, Ansh and Vickers, Daniel J. and Vaca-Revelo, Diego and Adam, Dimitrios and Yu, Haocheng and Lee, Hyeoksu and Chreim, Jose Rodolfo and {Carcana Barbosa}, Mirelys and Zhang, Yanjun and Cisneros-Garibay, Esteban and Gnanaskandan, Aswin and {Rodriguez Jr.}, Mauro and Budiardja, Reuben D. and Abbott, Stephen and Colonius, Tim and Bryngelson, Spencer H.},
  title = {{MFC 5.0: A}n exascale many-physics flow solver},
  file = {wilfong-mfc-26.pdf},
  journal = {Computer Physics Communications},
  year = {2026},
  volume = {322},
  pages = {110055},
  doi = {10.1016/j.cpc.2026.110055}
}

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. A previous work (Bryngelson et al., Comp. Phys. Comm. (2021)) published MFC 3.0 with numerous physical features, numerics, and scalability. MFC 5.0 is a marked update to MFC 3.0, including a broad set of well-established and novel physical models and numerical methods, and the introduction of XPU acceleration. We exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice. New physical features include the immersed boundary method, N-fluid phase change, Euler-Euler and Euler-Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan sees efficiencies within 5% of ideal to their full system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has improved, including continuous integration, ensuring code resilience and correctness through over 300 regression tests; metaprogramming, reducing code length and maintaining performance portability; and code generation for computing chemical reactions.

Cisneros-Garibay, E., Le Berre, H., Adam, D., Bryngelson, S. H., & Freund, J. B. (2026). Pyrometheus: Symbolic abstractions for XPU and automatically differentiated computation of combustion kinetics and thermodynamics. Computer Physics Communications, 320, 109987.

@article{Cisneros25,
  author = {Cisneros-Garibay, Esteban and {Le Berre}, H. and Adam, D. and Bryngelson, Spencer H. and Freund, Jonathan B.},
  title = {{Pyrometheus: S}ymbolic abstractions for {XPU} and automatically differentiated computation of combustion kinetics and thermodynamics},
  file = {cisneros-cpc-25.pdf},
  year = {2026},
  volume = {320},
  pages = {109987},
  doi = {10.1016/j.cpc.2025.109987},
  journal = {Computer Physics Communications}
}

The cost of combustion simulations is often dominated by the evaluation of net production rates of chemical species and mixture thermodynamics (thermochemistry). Execution on computing accelerators (XPUs) like graphic processing units (GPUs) can greatly reduce this cost. However, established thermochemistry software is not readily portable to such devices or sacrifices valuable analytical forms that enable differentiation for sensitivity analysis and implicit time integration. Symbolic abstractions are developed with corresponding transformations that enable computation on accelerators and automatic differentiation by avoiding premature specification of detail. The software package Pyrometheus is introduced as an implementation of these abstractions and their transformations for combustion thermochemistry. The formulation facilitates code generation from the symbolic representation of a specific thermochemical mechanism in multiple target languages, including Python, C++, and Fortran. Computational concerns are separated: the generated code processes array-valued expressions but does not specify their semantics. These semantics are provided by compatible array libraries, such as NumPy, Pytato, and Google JAX. Thus, the generated code retains a symbolic representation of the thermochemistry, which translates to computation on accelerators and CPUs and automatic differentiation. The design and operation of these symbolic abstractions and their companion tool, Pyrometheus, are discussed throughout. Roofline demonstrations show that the computation of chemical source terms within MFC, a Fortran-based flow solver we link to Pyrometheus, is performant.

Bryngelson, S. H. (2026). Fast integration method for averaging polydisperse bubble population dynamics. Computers & Fluids, 304, 106877.

@article{Bryngelson25,
  author = {Bryngelson, S. H.},
  title = {Fast integration method for averaging polydisperse bubble population dynamics},
  file = {bryngelson-caf-25.pdf},
  year = {2026},
  journal = {Computers \& Fluids},
  volume = {304},
  pages = {106877},
  doi = {10.1016/j.compfluid.2025.106877}
}

Ensemble-averaged polydisperse bubbly flow models require statistical moments of the evolving bubble size distribution. Under step forcing, these moments reach statistical equilibrium in finite time. However, the transitional phase before equilibrium and cases with time-dependent forcing are required to predict flow in engineering applications. Computing these moments is expensive because the integrands are highly oscillatory, even when the bubble dynamics are linear. Ensemble-averaged models compute these moments at each grid point and time step, making cost reduction important for large-scale bubbly flow simulations. Traditional methods evaluate the integrals via traditional quadrature rules. This approach requires a large number of quadrature nodes in the equilibrium bubble size, each equipped with its own advection partial differential equation (PDE), resulting in significant computational expense. We formulate a Levin collocation method to reduce this cost. Given the differential equation associated with the integrand, or moment, the method approximates it by evaluating its derivative via polynomial collocation. The differential matrix and amplitude function are well-suited to numerical differentiation via collocation, and so the computation is comparatively cheap. For an example excited polydisperse bubble population, the first moment is computed with the presented method at 0.001 relative error with 100 times fewer quadrature nodes than the trapezoidal rule. The gap increases for smaller target relative errors: the Levin method requires 10,000 times fewer points for a relative error at the single precision limit. The formulated method maintains constant cost as the integrands become more oscillatory with time, making it particularly attractive for long-time simulations. Mechanistically, the transient behavior of the moments is set by two effects: resonance detuning across bubble sizes, which causes phase mixing of oscillations, and viscous damping, which removes radial kinetic energy. The proposed formulation isolates the oscillations while keeping the remaining terms smooth, so accuracy does not deteriorate at late times.

Lee, M., Song, Z., Kocherla, S., Adams, A., Alexeev, A., & Bryngelson, S. H. (2026). A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method. Future Generation Computing Systems, 174, 107975.

@article{Lee25,
  author = {Lee, M. and Song, Z. and Kocherla, S. and Adams, A. and Alexeev, A. and Bryngelson, S. H.},
  title = {A multiple-circuit approach to quantum resource reduction with application to the quantum lattice {B}oltzmann method},
  file = {lee-fgcs-26.pdf},
  doi = {10.1016/j.future.2025.107975},
  journal = {Future Generation Computing Systems},
  pages = {107975},
  volume = {174},
  year = {2026}
}

This work proposes a multi-circuit quantum lattice Boltzmann method (QLBM) algorithm that leverages parallel quantum computing to reduce quantum resource requirements. Computational fluid dynamics (CFD) simulations often entail a large computational burden on classical computers. At present, these simulations can require up to trillions of grid points and millions of time steps. To reduce costs, novel architectures like quantum computers may be intrinsically more efficient for these computations. Current quantum algorithms for solving CFD problems are based on single quantum circuits and, in many cases, use lattice-based methods. Current quantum devices are adorned with sufficient noise to make large and deep circuits untenable. We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier–Stokes equations. The method, called QLBM-frugal, aims to create more practical quantum circuits and strategies for differential equation-based problems. The presented method is validated and demonstrated for 2D lid-driven cavity flow. The two-circuit algorithm shows a marked reduction in CNOT gates, which consume the majority of the runtime on quantum devices. Compared to the baseline QLBM technique, a two-circuit strategy shows increasingly large improvements in gate counts as the qubit size, or problem size, increases. For 64 lattice sites, the CNOT count was reduced by 35%, and the gate depth decreased by 16%. This strategy also enables concurrent circuit execution, further halving the seen gate depth.

2025

*Yu, H., *Chu, T., & Bryngelson, S. H. (2025). Energy dissipation mechanisms in an acoustically-driven slit. arXiv:2512.19507, *Equal contribution.

@unpublished{yu252,
  author = {*Yu, H. and *Chu, T. and Bryngelson, S. H.},
  title = {Energy dissipation mechanisms in an acoustically-driven slit},
  note = {arXiv:2512.19507, {*}Equal contribution},
  file = {yu-arxiv-252.pdf},
  arxiv = {arxiv.2512.19507},
  year = {2025},
  doi = {10.48550/arXiv.2512.19507}
}

We quantify how incident acoustic energy is converted into vortical motion and viscous dissipation for a two-dimensional plane-wave passing through a slit geometry. We perform direct numerical simulations over a broad parameter space in incident sound pressure level (ISPL), Strouhal number (St), and Reynolds number (Re). Spectral proper orthogonal decomposition (SPOD) yields energy-ranked coherent structures at each frequency, from which we construct mode-by-mode fields for spectral kinetic energy (KE) and viscous loss (VL) components to examine the mechanisms of acoustic absorption. At ISPL=150dB, the acoustic-hydrodynamic energy conversion is highest when the acoustic displacement amplitude is comparable to the slit thickness, corresponding to a Keulegan-Carpenter number of order unity. In this regime, the oscillatory boundary layer undergoes periodic separation, resulting in vortex shedding that dominates acoustic damping. VL accounts for 20-60% of the KE contribution. For higher acoustic frequencies, the confinement of the Stokes layer produces X-shaped near-slit modes, reducing the total energy input by approximately 50%. The influence of Re depends on amplitude. At ISPL=150dB, larger Re values correspond to suppressed broadband fluctuations and sharpened harmonic peaks. At ISPL = 120dB, the boundary layers remain attached, vortex shedding is weak, absorption monotonically scales with viscosity, and the Re- and St-dependencies become comparable. Across all conditions, more than 99% of the VL is confined to a compact region surrounding the slit mouth. The KE-VL spectra describe parameter regimes that enhance or suppress acoustic damping in slit geometries, providing a physically interpretable basis for acoustic-based design.

Yu, H., Ahuja, K., Sankar, L. L., & Bryngelson, S. H. (2025). Transmission of High-Amplitude Sound through Leakages of Ill-fitting Earplugs. arXiv:2510.16355.

@unpublished{yu25,
  author = {Yu, H. and Ahuja, K. and Sankar, L. L. and Bryngelson, S. H.},
  title = {Transmission of High-Amplitude Sound through Leakages of Ill-fitting Earplugs},
  note = {arXiv:2510.16355},
  file = {yu-arxiv-25.pdf},
  arxiv = {arXiv.2510.16355},
  year = {2025},
  doi = {10.48550/arXiv.2510.16355}
}

High sound pressure levels (SPL) pose notable risks in loud environments, particularly due to noise-induced hearing loss. Ill-fitting earplugs often lead to sound leakage, a phenomenon this study seeks to investigate. To validate our methodology, we first obtained computational and experimental acoustic transmission data for stand-alone slit resonators and orifices, for which extensive published data are readily available for comparison. We then examined the frequency-dependent acoustic power absorption coefficient and transmission loss (TL) across various leakage geometries, modeled using different orifice diameters. Experimental approaches spanned a frequency range of 1-5 kHz under SPL conditions of 120-150 dB. Key findings reveal that unsealed silicone rubber earplugs demonstrate an average TL reduction of approximately 18 dB at an overall incident SPL (OISPL) of 120 dB. Direct numerical simulations further highlight SPL-dependent acoustic dissipation mechanisms, showing the conversion of acoustic energy into vorticity in ill-fitting earplug models at an OISPL of 150 dB. These results highlight the role of earplug design for high-sound-pressure-level environments.

Jawetz, C. L., Song, Z., Alexeev, A., & Bryngelson, S. H. (2025). Quantum lattice Boltzmann algorithm for heat transfer with phase change. arXiv:2509.21630.

@unpublished{Jawetz25,
  author = {Jawetz, C. L. and Song, Z. and Alexeev, A. and Bryngelson, S. H.},
  title = {Quantum lattice {B}oltzmann algorithm for heat transfer with phase change},
  note = {arXiv:2509.21630},
  file = {jawetz-arxiv-25.pdf},
  arxiv = {arXiv.2509.21630},
  year = {2025},
  doi = {10.48550/arXiv.2509.21630}
}

Heat transfer involving phase change is computationally intensive due to moving phase boundaries, nonlinear computations, and time step restrictions. This paper presents a quantum lattice Boltzmann method (QLBM) for simulating heat transfer with phase change. The approach leverages the statistical nature of the lattice Boltzmann method (LBM) while addressing the challenges of nonlinear phase transitions in quantum computing. The method implements an interface-tracking strategy that partitions the problem into separate solid and liquid domains, enabling the algorithm to handle the discontinuity in the enthalpy-temperature relationship. We store phase change information in the quantum circuit to avoid frequent information exchange between classical and quantum hardware, a bottleneck in many quantum applications. Results from the implementation agree with both classical LBM and analytical solutions, demonstrating QLBM as an effective approach for analyzing thermal systems with phase transitions. Simulations using 17 lattice nodes with 51 qubits demonstrate root-mean-square (RMS) errors below 0.005 when compared against classical solutions. The method accurately tracks interface movement during phase transition.

Chu, T., Estrada, J. B., & Bryngelson, S. H. (2025). Accelerating Bayesian optimal experimental design via local radial basis functions: Application to soft material characterization. arXiv:2505.13283.

@unpublished{Chu25b,
  author = {Chu, T. and Estrada, J. B and Bryngelson, S H.},
  title = {Accelerating {B}ayesian optimal experimental design via local radial basis functions: {A}pplication to soft material characterization},
  note = {arXiv:2505.13283},
  file = {chu-rbf-arxiv-25.pdf},
  arxiv = {arXiv.2505.13283},
  year = {2025},
  doi = {10.48550/arXiv.2505.13283}
}

We develop a computational approach that significantly improves the efficiency of Bayesian optimal experimental design (BOED) using local radial basis functions (RBFs). The presented RBF-BOED method uses the intrinsic ability of RBFs to handle scattered parameter points, a property that aligns naturally with the probabilistic sampling inherent in Bayesian methods. By constructing accurate deterministic surrogates from local neighborhood information, the method enables high-order approximations with reduced computational overhead. As a result, computing the expected information gain (EIG) requires evaluating only a small uniformly sampled subset of prior parameter values, greatly reducing the number of expensive forward-model simulations needed. For demonstration, we apply RBF-BOED to optimize a laser-induced cavitation (LIC) experimental setup, where forward simulations follow from inertial microcavitation rheometry (IMR) and characterize the viscoelastic properties of hydrogels. Two experimental design scenarios, single- and multi-constitutive-model problems, are explored. Results show that EIG estimates can be obtained at just 8% of the full computational cost in a five-model problem within a two-dimensional design space. This advance offers a scalable path toward optimal experimental design in soft and biological materials.

Song, Z., Ren, H., Lee, M., Gard, B., Renaud, N., & Bryngelson, S. H. (2025). Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings . arXiv:2505.06455.

@unpublished{Song25,
  author = {Song, Zhixin and Ren, Hang and Lee, Melody and Gard, Bryan and Renaud, Nicolas and Bryngelson, Spencer H.},
  title = {Hadamard {R}andom {F}orest: {R}econstructing real-valued quantum states with exponential reduction in measurement settings
  },
  note = {arXiv:2505.06455},
  file = {song-arxiv-25.pdf},
  arxiv = {arXiv.2505.06455},
  year = {2025},
  doi = {10.48550/arXiv.2505.06455}
}

Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography (FQST) on an n qubit system requires an exponentially increasing overhead with O(3^n) distinct Pauli measurement settings to resolve all complex phases and reconstruct the density matrix. However, many appealing applications of quantum computing, such as quantum linear system algorithms, require only real-valued amplitudes. Here we introduce a novel readout method for real-valued quantum states that reduces measurement settings required for state vector reconstruction to O(n), while the post-processing cost remains exponential. This approach offers a substantial speedup over conventional tomography. We experimentally validate our method up to 10 qubits on the latest available IBM quantum processor and demonstrate that it accurately extracts key properties such as entanglement and magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles a numerical integration in certain cases and can be applied to extract nonlinear properties, which are important in application fields.

Chu, T., Wilfong, B., Koehler, T., McMullen, R. M., & Bryngelson, S. H. (2025). Competing mechanisms at vibrated interfaces of density-stratified fluids. Physical Review Fluids, 10, 093904.

@article{Chu25a,
  author = {Chu, T. and Wilfong, B. and Koehler, T. and McMullen, R. M. and Bryngelson, S. H.},
  title = {Competing mechanisms at vibrated interfaces of density-stratified fluids},
  file = {chu-prf-25.pdf},
  year = {2025},
  doi = {10.1103/r9b3-psg4},
  journal = {Physical Review Fluids},
  volume = {10},
  pages = {093904}
}

Fluid-fluid interfacial instability and subsequent fluid mixing are ubiquitous in nature and engineering. The hydrodynamic instability of fluid interfaces has long centered on the pressure gradient-driven long-wavelength Rayleigh-Taylor instability and the resonance-induced short-wavelength Faraday instability. However, neither instability alone can explain the dynamics when both mechanisms are present. We identify a previously unseen multi-modal instability emerging from their coexistence. When the denser fluid is polydimethylsiloxane, the mixed region at a high density contrast (Atwood number = 0.9) spans a vibration amplitude range approximately twice the gravitational acceleration. Using Floquet stability analysis, we show how vibrations govern transitions between the RT and Faraday instabilities, leading to contention between these instabilities rather than resonant enhancement. The initial transient growth is represented by the exponential modal growth of the most unstable Floquet exponent, along with its accompanying periodic behavior. Direct numerical simulations validate these findings and track interface breakup into the multiscale and nonlinear regimes. Specifically, we show that growing RT modes nonlinearly suppresses Faraday responses even when the initial growth rate of the Faraday instability is 3.63 times that of RT, so a bidirectional competition hinders their sustained coexistence.

Zhu, Z., Remillard, S., Abeid, B. A., Frolkin, D., Bryngelson, S. H., Yang, J., Rodriguez Jr., M., & Estrada, J. B. (2025). Parsimonious inertial cavitation rheometry via bubble collapse time. Soft Matter, 21(34), 6717–6734.

@article{Zhu25,
  author = {Zhu, Z. and Remillard, S. and Abeid, B. A. and Frolkin, D. and Bryngelson, S. H. and Yang, J. and {Rodriguez Jr.}, M. and Estrada, J. B.},
  title = {Parsimonious inertial cavitation rheometry via bubble collapse time},
  journal = {Soft Matter},
  doi = {10.1039/D5SM00397K},
  volume = {21},
  number = {34},
  pages = {6717-6734},
  year = {2025},
  file = {zhu-soft-25.pdf}
}

The rapid and accurate characterization of soft, viscoelastic materials at high strain rates is of interest in biological and engineering applications such as assessing the extent of non-invasive tissue surgery completion and developing injury criteria for the mitigation of blast injuries. The inertial microcavitation rheometry technique (IMR, Estrada et al. 2018) allows for the minimally invasive characterization of local viscoelastic properties at strain rates up to 100M units per second. However, IMR relies on bright-field videography of a sufficiently translucent sample at approximately 1 million frames per second and a simulation-dependent fit optimization process that can require hours of post-processing. We present an IMR-style technique that parsimoniously characterizes viscoelastic models. The approach uses experimental advancements to accurately estimate the time to first collapse of the laser-induced cavity. A theoretical energy balance analysis yields an approximate collapse time based on the material viscoelasticity parameters. The method closely matches the accuracy of the original IMR procedure while decreasing the computational cost from hours to seconds for the Kelvin–Voigt model and potentially reducing dependence on high-speed videography. This technique can enable nearly real-time characterization of a broader range of soft, viscoelastic hydrogels and biological materials.

Chu, T., Estrada, J. B., & Bryngelson, S. H. (2025). Bayesian optimal design accelerates discovery of soft material properties from bubble dynamics. Computational Mechanics, 76, 431–447.

@article{Chu25c,
  author = {Chu, T. and Estrada, J. B. and Bryngelson, S. H.},
  title = {Bayesian optimal design accelerates discovery of soft material properties from bubble dynamics},
  doi = {10.1007/s00466-025-02606-4},
  file = {chu-cm-25.pdf},
  journal = {Computational Mechanics},
  volume = {76},
  pages = {431-447},
  year = {2025}
}

An optimal sequential experimental design approach is developed to computationally characterize soft material properties at the high strain rates associated with bubble cavitation. The approach involves optimal design and model inference. The optimal design strategy maximizes the expected information gain in a Bayesian statistical setting to design experiments that provide the most informative cavitation data about unknown soft material properties. We infer constitutive models by characterizing the associated viscoelastic properties from measurements via a hybrid ensemble-based 4D-Var method (En4D-Var). The inertial microcavitation-based high strain-rate rheometry (IMR) method (Estrada et al. J Mech Phys Solids 112:291–317, 2018) simulates the bubble dynamics under laser-induced cavitation. We use experimental measurements to create synthetic data representing the viscoelastic behavior of stiff and soft polyacrylamide hydrogels under realistic uncertainties. The synthetic data are seeded with larger errors than state-of-the-art measurements yet matches known material properties, reaching 1 percent relative error within 10 sequential designs (experiments). We discern between two seemingly equally plausible constitutive models, Neo-Hookean Kelvin–Voigt and quadratic Kelvin–Voigt, with a probability of correctness larger than 99 percent in the same number of experiments. This strategy discovers soft material properties, including discriminating between constitutive models and discerning their parameters, using only a few experiments.

Song, Z., Deaton, R., Gard, B., & Bryngelson, S. H. (2025). Incompressible Navier–Stokes solve on noisy quantum hardware via a hybrid quantum–classical scheme. Computers & Fluids, 288, 106507.

@article{Song25b,
  author = {Song, Z. and Deaton, R. and Gard, B. and Bryngelson, S. H.},
  title = {Incompressible {N}avier--{S}tokes solve on noisy quantum hardware via a hybrid quantum--classical scheme},
  journal = {Computers \& Fluids},
  pages = {106507},
  file = {song-caf-25.pdf},
  volume = {288},
  doi = {10.1016/j.compfluid.2024.106507},
  year = {2025}
}

Partial differential equation solvers are required to solve the Navier–Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable exponential speedups over algorithms on classical computers. However, current and foreseeable quantum hardware introduce noise into computations, requiring algorithms that make judicious use of quantum resources: shallower circuit depths and fewer qubits. Under these restrictions, variational algorithms are more appropriate and robust. This work presents a hybrid quantum–classical algorithm for the incompressible Navier–Stokes equations. A classical device performs nonlinear computations, and a quantum one uses a variational solver for the pressure Poisson equation. A lid-driven cavity problem benchmarks the method. We verify the algorithm via noise-free simulation and test it on noisy IBM superconducting quantum hardware. Results show that high-fidelity results can be achieved via this approach, even on current quantum devices. Multigrid preconditioning of the Poisson problem helps avoid local minima and reduces resource requirements for the quantum device. A quantum state readout technique called HTree is used for the first time on a physical problem. HTree is appropriate for real-valued problems and achieves linear complexity in the qubit count, making the Navier–Stokes solve further tractable on current quantum devices. We compare the quantum resources required for near-term and fault-tolerant solvers to determine quantum hardware requirements for fluid simulations with complexity improvements.

Wilfong, B., Radhakrishnan, A., Le Berre, H., Vickers, D. J., Prathi, T., Tselepidis, N., Dorschner, B., Budiardja, R., Cornille, B., Abbott, S., *Schäfer, F., & *Bryngelson, S. H. (2025). Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization. Proceedings of SC ’25: The International Conference for High Performance Computing, Networking, Storage and Analysis, 14–24. *Equal contribution.

@inproceedings{Wilfong25,
  author = {Wilfong, Benjamin and Radhakrishnan, Anand and {Le Berre}, Henry and Vickers, Daniel J. and Prathi, Tanush and Tselepidis, Nikolaos and Dorschner, Benedikt and Budiardja, Reuben and Cornille, Brian and Abbott, Stephen and {*}Schäfer, F. and {*}Bryngelson, S. H.},
  title = {Simulating many-engine spacecraft: {E}xceeding 1 quadrillion degrees of freedom via information geometric regularization},
  booktitle = {Proceedings of SC '25: The International Conference for High Performance Computing, Networking, Storage and Analysis},
  note = {{*}Equal contribution},
  file = {wilfong-sc25-gb.pdf},
  year = {2025},
  pages = {14--24},
  doi = {10.1145/3712285.3771783},
  keywords = {heavyref}
}

We present an optimized implementation of the recently proposed information geometric regularization (IGR) for unprecedented scale simulation of compressible fluid flows applied to multi-engine spacecraft boosters. We improve upon state-ofthe-art computational fluid dynamics (CFD) techniques along computational cost, memory footprint, and energy-to-solution metrics. Unified memory on coupled CPU–GPU or APU platforms increases problem size with negligible overhead. Mixed half/singleprecision storage and computation on well-conditioned numerics is used. We simulate flow at 200 trillion grid points and 1 quadrillion degrees of freedom, exceeding the current record by a factor of 20. A factor of 4 wall-time speedup is achieved over optimized baselines. Ideal weak scaling is seen on OLCF Frontier, LLNL El Capitan, and CSCS Alps using the full systems. Strong scaling is near ideal at extreme conditions, including 80% efficiency on CSCS Alps with an 8 node baseline and stretching to the full system.

Wilfong, B., Radhakrishnan, A., Le Berre, H. A., Prathi, T., Abbott, S., & Bryngelson, S. H. (2025). Testing and benchmarking emerging supercomputers via the MFC flow solver. SC Workshops ’25: Proceedings of the SC ’25 Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis, 669–677.

@inproceedings{proceeding_27,
  title = {Testing and benchmarking emerging supercomputers via the {MFC} flow solver},
  author = {Wilfong, B. and Radhakrishnan, A. and {Le Berre}, H. A. and Prathi, T. and Abbott, S. and Bryngelson, S. H.},
  booktitle = {SC Workshops '25: Proceedings of the SC '25 Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis},
  year = {2025},
  doi = {10.1145/3731599.3767424},
  pages = {669--677},
  file = {wilfong-SC-HPCTESTS-25.pdf},
  keywords = {heavyref}
}

Deploying new supercomputers requires testing and evaluation via application codes. Portable, user-friendly tools enable evaluation, and the Multicomponent Flow Code (MFC), a computational fluid dynamics (CFD) code, addresses this need. MFC is adorned with a toolchain that automates input generation, compilation, batch job submission, regression testing, and benchmarking. The toolchain design enables users to evaluate compiler-hardware combinations for correctness and performance with limited software engineering experience. As with other PDE solvers, wall time per spatially discretized grid point serves as a figure of merit. We present MFC benchmarking results for five generations of NVIDIA GPUs, three generations of AMD GPUs, and various CPU architectures, utilizing Intel, Cray, NVIDIA, AMD, and GNU compilers. These tests have revealed compiler bugs and regressions on recent machines such as Frontier and El Capitan. MFC has benchmarked approximately 50 compute devices and 5 flagship supercomputers.

2024

Shahane, S., Chammas, S., Bezgin, D. A., Buhendwa, A. B., Schmidt, S. J., Adams, N. A., Bryngelson, S. H., Chen, Y.-F., Wang, Q., Sha, F., & Zepeda-Núñez, L. (2024). Rational-WENO: A lightweight, physically-consistent three-point weighted essentially non-oscillatory scheme. arXiv.2409.09217.

@report{Shahane24,
  author = {Shahane, S. and Chammas, S. and Bezgin, D. A. and Buhendwa, A. B. and Schmidt, S. J. and Adams, N. A. and Bryngelson, S. H. and Chen, Y.-F. and Wang, Q. and Sha, F. and Zepeda-Núñez, L.},
  title = {{Rational-WENO: A} lightweight, physically-consistent three-point weighted essentially non-oscillatory scheme},
  doi = {10.48550/arXiv.2409.09217},
  file = {shahane-arxiv-24.pdf},
  arxiv = {arXiv.2409.09217},
  institution = {arXiv.2409.09217},
  year = {2024}
}

Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness of the solution, dynamically adapting the stencil weights based on local solution features. As rational neural networks can represent fast transitions between smooth and sharp regimes, this approach achieves a granular reconstruction with significantly reduced dissipation, improving the accuracy of the simulation. The network is trained offline on a carefully chosen dataset of analytical functions, bypassing the need for differentiable solvers. We also propose a robust model selection criterion based on estimates of the interpolation’s convergence order on a set of test functions, which correlates better with the model performance in downstream tasks. We demonstrate the effectiveness of our approach on several one-, two-, and three-dimensional fluid flow problems: our scheme generalizes across grid resolutions while handling smooth and discontinuous solutions. In most cases, our rational network-based scheme achieves higher accuracy than conventional WENO3 with the same stencil size, and in a few of them, it achieves accuracy comparable to WENO5, which uses a larger stencil.

Kocherla, S., Song, Z., Chrit, F. E., Gard, B., Dumitrescu, E. F., Alexeev, A., & Bryngelson, S. H. (2024). Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations. AVS Quantum Science, 6, 033806.

@article{Kocherla24,
  author = {Kocherla, S. and Song, Z. and Chrit, F. E. and Gard, B. and Dumitrescu, E. F. and Alexeev, A. and Bryngelson, S. H.},
  title = {Fully quantum algorithm for mesoscale fluid simulations
  with application to partial differential equations},
  doi = {10.1116/5.0217675},
  file = {kocherla-AVS-24.pdf},
  year = {2024},
  volume = {6},
  pages = {033806},
  journal = {AVS Quantum Science}
}

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. This method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers’ equations on differ

Liu, J., Schäfer, F., Bryngelson, S. H., Zaki, T. A., & Mani, A. (2024). Adjoint-based computation of nonlocal eddy viscosity in turbulent channel flow. Physical Review Fluids, 9, 094606.

@article{Liu24,
  author = {Liu, J. and Sch\"afer, F. and Bryngelson, S. H. and Zaki, T. A. and Mani, A.},
  title = {Adjoint-based computation of nonlocal eddy viscosity in turbulent channel flow},
  year = {2024},
  journal = {Physical Review Fluids},
  volume = {9},
  pages = {094606},
  doi = {10.1103/PhysRevFluids.9.094606},
  file = {liu-PRF-24.pdf}
}

Reynolds-averaged Navier–Stokes (RANS) closure operators are generally nonlocal and anisotropic for many flows, including wall-bounded turbulence. The macroscopic forcing method (MFM) and Green’s function-based approaches examine these effects using forced direct numerical simulations. For these approaches, the number of simulations required to compute the nonlocal and anisotropic eddy viscosity is equal to the number of degrees of freedom in the averaged space. We reduce the computational cost by introducing an adjoint-based formulation of MFM to obtain the nonlocal and anisotropic eddy viscosity at any Reynolds stress location using a single simulation. We then quantify the streamwise and wall-normal nonlocal eddy viscosity at near-wall locations in turbulent channel flow at shear Reynolds number 180. We demonstrate that the upstream nonlocality is not fully described by Lagrangian transport. We also quantify the significant differences in the upstream nonlocality between various components of the eddy viscosity tensor. Our results can be used to guide closure modeling, including the lengthscales and timescales used in Reynolds stress models.

Radhakrishnan, A., Le Berre, H., Wilfong, B., Spratt, J.-S., Rodriguez Jr., M., Colonius, T., & Bryngelson, S. H. (2024). Method for portable, scalable, and performant GPU-accelerated simulation of multiphase compressible flow. Computer Physics Communications, 302, 109238.

@article{Radhakrishnan24,
  author = {Radhakrishnan, A. and {Le Berre}, H. and Wilfong, B. and Spratt, J.-S. and {Rodriguez Jr.}, M. and Colonius, T. and Bryngelson, S. H.},
  title = {Method for portable, scalable, and performant {GPU}-accelerated simulation of multiphase compressible flow},
  file = {radhakrishnan-CPC-24.pdf},
  year = {2024},
  volume = {302},
  doi = {10.1016/j.cpc.2024.109238},
  journal = {Computer Physics Communications},
  pages = {109238}
}

Multiphase compressible flows are often characterized by a broad range of space and time scales. Thus entailing large grids and small time steps, simulations of these flows on CPU-based clusters can thus take several wall-clock days. Offloading the compute kernels to GPUs appears attractive but is memory-bound for standard finite-volume and -difference methods, damping speed-ups. Even when realized, faster GPU-based kernels lead to more intrusive communication and I/O times. We present a portable strategy for GPU acceleration of multiphase compressible flow solvers that addresses these challenges and obtains large speedups at scale. We use OpenACC for portable offloading of all compute kernels while maintaining low-level control when needed. An established Fortran preprocessor and metaprogramming tool, Fypp, enables otherwise hidden compile-time optimizations. This strategy exposes compile-time optimizations and high memory reuse while retaining readable, maintainable, and compact code. Remote direct memory access, realized via CUDA-aware MPI, reduces communication times. We implement this approach in the open-source solver MFC. Metaprogramming-based preprocessing results in an 8-times speedup of the most expensive kernels, 46% of peak FLOPs on NVIDIA GPUs, and high arithmetic intensity (about 10 FLOPs/byte). In representative simulations, a single A100 GPU is 300-times faster than an Intel Xeon CPU core, corresponding to a 9-times speedup for a single A100 compared to the entire CPU die. At the same time, near-ideal (97%) weak scaling is observed for at least 13824 GPUs on Summit. A strong scaling efficiency of 84% is retained for an 8-times increase in GPU count. Collective I/O, implemented via MPI3, helps ensure negligible contribution of data transfers. Large many-GPU simulations of compressible (solid-)liquid-gas flows demonstrate the practical utility of this strategy.

Sinha, A., & Bryngelson, S. H. (2024). Neural networks can be FLOP-efficient integrators of 1D oscillatory integrands. Transactions on Machine Learning Research.

@article{Sinha24,
  title = {Neural networks can be {FLOP}-efficient integrators of {1D} oscillatory integrands},
  author = {Sinha, A. and Bryngelson, S. H.},
  journal = {Transactions on Machine Learning Research},
  issn = {2835-8856},
  year = {2024},
  file = {sinha-TMLR-24.pdf},
  link = {https://openreview.net/pdf?id=5psgQEHn6t}
}

We demonstrate that neural networks can be FLOP-efficient integrators of one-dimensional oscillatory integrands. We train a feed-forward neural network to compute integrals of highly oscillatory 1D functions. The training set is a parametric combination of functions with varying characters and oscillatory behavior degrees. Numerical examples show that these networks are FLOP-efficient for sufficiently oscillatory integrands with an average FLOP gain of 1000 FLOPs. The network calculates oscillatory integrals better than traditional quadrature methods under the same computational budget or number of floating point operations. We find that feed-forward networks of 5 hidden layers are satisfactory for a relative accuracy of 0.001. The computational burden of inference of the neural network is relatively small, even compared to inner-product pattern quadrature rules. We postulate that our result follows from learning latent patterns in the oscillatory integrands that are otherwise opaque to traditional numerical integrators.

*Bryngelson, S. H., *Schäfer, F., Liu, J., & Mani, A. (2024). Fast Macroscopic Forcing Method. Journal of Computational Physics, 499, 112721. *Equal contribution.

@article{Bryngelson24,
  author = {{*}Bryngelson, S. H. and {*}Sch{\"a}fer, F. and Liu, J. and Mani, A.},
  title = {Fast {M}acroscopic {F}orcing {M}ethod},
  journal = {Journal of Computational Physics},
  file = {bryngelson-JCP-24.pdf},
  year = {2024},
  volume = {499},
  pages = {112721},
  doi = {10.1016/j.jcp.2023.112721},
  note = {{*}Equal contribution}
}

The macroscopic forcing method (MFM) of Mani and Park (2021) and similar methods for obtaining turbulence closure operators, such as the Green’s function-based approach of Hamba (1995), recover reduced solution operators from repeated direct numerical simulations (DNS). MFM has already been used to successfully quantify Reynolds-averaged Navier-Stokes (RANS)-like operators for homogeneous isotropic turbulence and turbulent channel flows. Standard algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of freedom in the RANS space) and conduct a corresponding fine-scale simulation (i.e., DNS), which is expensive. We combine this method with an approach recently proposed by Schäfer and Owhadi (2023) to recover elliptic integral operators from a polylogarithmic number of matrix-vector products. The resulting Fast MFM introduced in this work applies sparse reconstruction to expose local features in the closure operator and reconstructs this coarse-grained differential operator in only a few matrix-vector products and correspondingly, a few MFM simulations. For flows with significant nonlocality, the algorithm first “peels” long-range effects with dense matrix-vector products to expose a more local operator. We demonstrate the algorithm’s performance for scalar transport in a laminar channel flow and momentum transport in a turbulent channel flow. For these problems, we recover eddy diffusivity- and eddy viscosity-like operators, respectively, at 1 percent of the cost of computing the exact operator via a brute-force approach for the laminar channel flow problem and 13 percent for the turbulent one. We observe that we can reconstruct these operators with an increase in accuracy by about a factor of 100 over randomized low-rank methods. Applying these operators to compute the averaged fields of interest has visually indistinguishable behavior from the exact solution. Our results show that a similar number of simulations are required to reconstruct the operators to the same accuracy under grid refinement. Thus, the accuracy corresponds to the physics of the problem, not the numerics. We glean that for problems in which the RANS space is reducible to one dimension, eddy diffusivity and eddy viscosity operators can be reconstructed with reasonable accuracy using only a few simulations, regardless of simulation resolution or degrees of freedom.

Bati, A., & Bryngelson, S. H. (2024). RoseNNa: A performant, portable library for neural network inference with application to computational fluid dynamics. Computer Physics Communications, 296, 109052.

@article{Bati24,
  author = {Bati, A. and Bryngelson, S. H.},
  title = {{RoseNNa: A} performant, portable library for neural network inference with
  application to computational fluid dynamics},
  journal = {Computer Physics Communications},
  volume = {296},
  pages = {109052},
  file = {bati-CPC-24.pdf},
  year = {2024},
  doi = {10.1016/j.cpc.2023.109052}
}

The rise of neural network-based machine learning ushered in high-level libraries, including TensorFlow and PyTorch, to support their functionality. Computational fluid dynamics (CFD) researchers have benefited from this trend and produced powerful neural networks that promise shorter simulation times. For example, multilayer perceptrons (MLPs) and Long Short Term Memory (LSTM) recurrent-based (RNN) architectures can represent sub-grid physical effects, like turbulence. Implementing neural networks in CFD solvers is challenging because the programming languages used for machine learning and CFD are mostly non-overlapping, We present the roseNNa library, which bridges the gap between neural network inference and CFD. RoseNNa is a non-invasive, lightweight (1000 lines), and performant tool for neural network inference, with focus on the smaller networks used to augment PDE solvers, like those of CFD, which are typically written in C/C++ or Fortran. RoseNNa accomplishes this by automatically converting trained models from typical neural network training packages into a high-performance Fortran library with C and Fortran APIs. This reduces the effort needed to access trained neural networks and maintains performance in the PDE solvers that CFD researchers build and rely upon. Results show that RoseNNa reliably outperforms PyTorch (Python) and libtorch (C++) on MLPs and LSTM RNNs with less than 100 hidden layers and 100 neurons per layer, even after removing the overhead cost of API calls. Speedups range from a factor of about 10 and 2 faster than these established libraries for the smaller and larger ends of the neural network size ranges tested.

Wilfong, B., Radhakrishnan, A., Le Berre, H. A., Abbott, S., Budiardja, R. D., & Bryngelson, S. H. (2024). OpenACC offloading of the MFC compressible multiphase flow solver on AMD and NVIDIA GPUs. SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis, 1923–1933.

@inproceedings{proceeding_25,
  title = {{OpenACC} offloading of the {MFC} compressible multiphase flow solver on {AMD} and {NVIDIA GPUs}},
  author = {Wilfong, B. and Radhakrishnan, A. and {Le Berre}, H. A. and Abbott, S. and Budiardja, R. D. and Bryngelson, S. H.},
  booktitle = {SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis},
  year = {2024},
  pages = {1923--1933},
  doi = {10.1109/SCW63240.2024.00242},
  file = {wilfong-SC-24.pdf},
  keywords = {heavyref}
}

GPUs are the heart of the latest generations of supercomputers. We efficiently accelerate a compressible multiphase flow solver via OpenACC on NVIDIA and AMD Instinct GPUs. Optimization is accomplished by specifying the directive clauses ’gang vector’ and ’collapse’. Further speedups of six and ten times are achieved by packing user-defined types into coalesced multidimensional arrays and manual inlining via metaprogramming. Additional optimizations yield seven-times speedup in array packing and thirty-times speedup of select kernels on Frontier. Weak scaling efficiencies of 97% and 95% are observed when scaling to 50% of Summit and 95% of Frontier. Strong scaling efficiencies of 84% and 81% are observed when increasing the device count by a factor of 8 and 16 on V100 and MI250X hardware. The strong scaling efficiency of AMD’s MI250X increases to 92% when increasing the device count by a factor of 16 when GPU-aware MPI is used for communication.

2023

Firouznia, M., Bryngelson, S. H., & Saintillan, D. (2023). A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops. Journal of Computational Physics, 489, 112248.

@article{firouznia23,
  author = {Firouznia, M. and Bryngelson, S. H. and Saintillan, D.},
  title = {A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops},
  year = {2023},
  pages = {112248},
  volume = {489},
  file = {firouznia-JCP-23.pdf},
  journal = {Journal of Computational Physics},
  doi = {10.1016/j.jcp.2023.112248}
}

A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling of interfacial charge transport and fluid flow can trigger electrohydrodynamic instabilities that lead to shape deformations and complex dynamics. We present a spectral boundary integral method to simulate droplet electrohydrodynamics in a uniform electric field. All physical variables, such as drop shape and interfacial charge density, are represented using spherical harmonic expansions. In addition to its exponential accuracy, the spectral representation affords a nondissipative dealiasing method required for numerical stability. A comprehensive charge transport model, valid under a wide range of electric field strengths, accounts for charge relaxation, Ohmic conduction, and surface charge convection by the flow. A shape reparametrization technique enables the exploration of significant droplet deformation regimes. For low-viscosity drops, the convection by the flow drives steep interfacial charge gradients near the drop equator. This introduces numerical ringing artifacts we treat via a weighted spherical harmonic expansion, resulting in solution convergence. The method and simulations are validated against experimental data and analytical predictions in the axisymmetric Taylor and Quincke electrorotation regimes.

Bryngelson, S. H., Fox, R. O., & Colonius, T. (2023). Conditional moment methods for polydisperse cavitating flows. Journal of Computational Physics, 477, 111917.

@article{Bryngelson23,
  author = {Bryngelson, S. H. and Fox, R. O. and Colonius, T.},
  title = {Conditional moment methods for polydisperse cavitating flows},
  file = {bryngelson-JCP-23.pdf},
  journal = {Journal of Computational Physics},
  year = {2023},
  volume = {477},
  doi = {10.1016/j.jcp.2023.111917},
  pages = {111917}
}

The dynamics of cavitation bubbles are important in many flows, but their small sizes and high number densities often preclude direct numerical simulation. We present a computational model that averages their effect on the flow over larger spatiotemporal scales. The model is based on solving a generalized population balance equation (PBE) for nonlinear bubble dynamics and explicitly represents the evolving probability density of bubble radii and radial velocities. Conditional quadrature-based moment methods (QBMMs) are adapted to solve this PBE. A one-way-coupled bubble dynamics problem demonstrates the efficacy of different QBMMs for the evolving bubble statistics. Results show that enforcing hyperbolicity during moment inversion (CHyQMOM) provides comparable model-form accuracy to the traditional conditional method of moments and decreases computational costs by about ten times for a broad range of test cases. The CHyQMOM-based computational model is implemented in MFC, an open-source multi-phase and high-order-accurate flow solver. We assess the effect of the model and its parameters on a two-way coupled bubble screen flow problem.

Panchal, A., Bryngelson, S. H., & Menon, S. (2023). A seven-equation diffused interface method for resolved multiphase flows. Journal of Computational Physics, 475, 111870.

@article{Panchal23,
  author = {Panchal, A. and Bryngelson, S. H. and Menon, S.},
  title = {A seven-equation diffused interface method for resolved multiphase flows},
  journal = {Journal of Computational Physics},
  file = {panchal-JCP-23.pdf},
  volume = {475},
  pages = {111870},
  year = {2023},
  doi = {10.1016/j.jcp.2022.111870}
}

The seven-equation model is a compressible multiphase formulation that allows for phasic velocity and pressure disequilibrium. These equations are solved using a diffused interface method that models resolved multiphase flows. Novel extensions are proposed for including the effects of surface tension, viscosity, multi-species, and reactions. The allowed non-equilibrium of pressure in the seven-equation model provides numerical stability in strong shocks and allows for arbitrary and independent equations of states. A discrete equations method (DEM) models the fluxes. We show that even though stiff pressure- and velocity-relaxation solvers have been used, they are not needed for the DEM because the non-conservative fluxes are accurately modeled. An interface compression scheme controls the numerical diffusion of the interface, and its effects on the solution are discussed. Test cases are used to validate the computational method and demonstrate its applicability. They include multiphase shock tubes, shock propagation through a material interface, a surface-tension-driven oscillating droplet, an accelerating droplet in a viscous medium, and shock-detonation interacting with a deforming droplet. Simulation results are compared against exact solutions and experiments when possible.

Elwasif, W., Bastrakov, S., Bryngelson, S. H., Bussmann, M., Chandrasekaran, S., Ciorba, F., Clark, M. A., Debus, A., Godoy, W., Hagerty, N., Hammond, J., Hardy, D., Harris, J. A., Hernandez, O., Joo, B., Keller, S., Kent, P., Le Berre, H., Lebrun-Grandie, D., MacCarthy, E., Vergara, V. G. M., Messer, B., Miller, R., Oral, S., Piccinali, J.-G., Radhakrishnan, A., Simsek, O., Spiga, F., Steiniger, K., Stephan, J., Stone, J. E., Trott, C., Widera, R., & Young, J. (2023). Early application experiences on a modern GPU-accelerated Arm-based HPC platform. HPC Asia ’23, 35–49.

@inproceedings{proceeding_15,
  author = {Elwasif, W. and Bastrakov, S. and Bryngelson, S. H. and Bussmann, M. and Chandrasekaran, S. and Ciorba, F. and Clark, M. A. and Debus, A. and Godoy, W. and Hagerty, N. and Hammond, J. and Hardy, D. and Harris, J. A. and Hernandez, O. and Joo, B. and Keller, S. and Kent, P. and {Le Berre}, H. and Lebrun-Grandie, D. and MacCarthy, E. and Vergara, V. G. Melesse and Messer, B. and Miller, R. and Oral, S. and Piccinali, J.-G. and Radhakrishnan, A. and Simsek, O. and Spiga, F. and Steiniger, K. and Stephan, J. and Stone, J. E. and Trott, C. and Widera, R. and Young, J.},
  title = {Early application experiences on a modern {GPU}-accelerated {A}rm-based {HPC} platform},
  booktitle = {HPC Asia '23},
  series = {International Workshop on Arm-based HPC: Practice and Experience (IWAHPCE)},
  file = {elwasif-IWAHPCE-23.pdf},
  doi = {10.1145/3581576.3581621},
  address = {Singapore},
  year = {2023},
  pages = {35-49},
  acceptrate = {44},
  keywords = {heavyref}
}

This paper assesses and reports the experience of ten teams working to port, validate, and benchmark several High Performance Computing applications on a novel GPU-accelerated Arm testbed system. The testbed consists of eight NVIDIA Arm HPC Developer Kit systems, each one equipped with a server-class Arm CPU from Ampere Computing and two data center GPUs from NVIDIA Corp. The systems are connected together using InfiniBand interconnect. The selected applications and mini-apps are written using several programming languages and use multiple accelerator-based programming models for GPUs such as CUDA, OpenACC, and OpenMP offloading. Working on application porting requires a robust and easy-to-access programming environment, including a variety of compilers and optimized scientific libraries. The goal of this work is to evaluate platform readiness and assess the effort required from developers to deploy well-established scientific workloads on current and future generation Arm-based GPU-accelerated HPC systems. The reported case studies demonstrate that the current level of maturity and diversity of software and tools is already adequate for large-scale production deployments.

Zeng, Q., Kothari, Y., Bryngelson, S. H., & Schäfer, F. (2023). Competitive physics informed networks. International Conference on Learning Representations (ICLR). arXiv:2204.11144.

@inproceedings{Zeng23,
  author = {Zeng, Q. and Kothari, Y. and Bryngelson, S. H. and Sch{\"a}fer, F.},
  title = {Competitive physics informed networks},
  booktitle = {International Conference on Learning Representations (ICLR)},
  file = {zeng-ICLR-23.pdf},
  note = {arXiv:2204.11144},
  address = {Kigali, Rwanda},
  year = {2023},
  link = {https://openreview.net/pdf?id=z9SIj-IM7tn},
  keywords = {heavyref}
}

Physics Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by representing them as neural networks. The original PINN implementation does not provide high accuracy, typically attaining about 0.1 percent relative error. We formulate and test an adversarial approach called competitive PINNs (CPINNs) to overcome this limitation. CPINNs train a discriminator that is rewarded for predicting PINN mistakes. The discriminator and PINN participate in a zero-sum game with the exact PDE solution as an optimal strategy. This approach avoids the issue of squaring the large condition numbers of PDE discretizations. Numerical experiments show that a CPINN trained with competitive gradient descent can achieve errors two orders of magnitude smaller than that of a PINN trained with Adam or stochastic gradient descent.

2022

Charalampopoulos, A., Bryngelson, S. H., Colonius, T., & Sapsis, T. P. (2022). Hybrid quadrature moment method for accurate and stable representation of non-Gaussian processes and their dynamics. Philosophical Transactions of the Royal Society A, 380(2229).

@article{Charalampopoulos21,
  author = {Charalampopoulos, A. and Bryngelson, S. H. and Colonius, T. and Sapsis, T. P.},
  title = {Hybrid quadrature moment method for accurate and stable representation of non-{G}aussian processes and their dynamics},
  file = {charalampopoulos-RSA-21.pdf},
  journal = {Philosophical Transactions of the Royal Society A},
  year = {2022},
  volume = {380},
  number = {2229},
  doi = {10.1098/rsta.2021.0209}
}

Solving the population balance equation (PBE) for the dynamics of a dispersed phase coupled to a continuous fluid is expensive. Still, one can reduce the cost by representing the evolving particle density function in terms of its moments. In particular, quadrature-based moment methods (QBMMs) invert these moments with a quadrature rule, approximating the required statistics. QBMMs have been shown to accurately model sprays and soot with a relatively compact set of moments. However, significantly non-Gaussian processes such as bubble dynamics lead to numerical instabilities when extending their moment sets accordingly. We solve this problem by training a recurrent neural network (RNN) that adjusts the QBMM quadrature to evaluate unclosed moments with higher accuracy. The proposed method is tested on a simple model of bubbles oscillating in response to a temporally fluctuating pressure field. The approach decreases model-form error by a factor of 10 when compared to traditional QBMMs. It is both numerically stable and computationally efficient since it does not expand the baseline moment set. Additional quadrature points are also assessed, optimally placed and weighted according to an additional RNN. These points further decrease the error at low cost since the moment set is again unchanged.

2021

Spratt, J.-S., Rodriguez, M., Schmidmayer, K., Bryngelson, S. H., Yang, J., Franck, C., & Colonius, T. (2021). Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations. Journal of the Mechanics and Physics of Solids, 152, 104455.

@article{Spratt21,
  author = {Spratt, J.-S. and Rodriguez, M. and Schmidmayer, K. and Bryngelson, S. H. and Yang, J. and Franck, C. and Colonius, T.},
  title = {Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations},
  journal = {Journal of the Mechanics and Physics of Solids},
  file = {spratt-JMPS-21.pdf},
  year = {2021},
  volume = {152},
  pages = {104455},
  doi = {10.1016/j.jmps.2021.104455}
}

Bubble cavitation can induce such strain rates, and the resulting bubble dynamics are sensitive to the material properties. Thus, in principle, these properties can be inferred via measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such bubble-dynamic high-strain-rate rheometry by using least-squares shooting to minimize the difference between simulated and experimental bubble radius histories. We generalize their technique to account for additional uncertainties in the model, initial conditions, and material properties needed to uniquely simulate the bubble dynamics. Ensemble-based data assimilation minimizes the computational expense associated with the bubble cavitation model. We test an ensemble Kalman filter (EnKF), an iterative ensemble Kalman smoother (IEnKS), and a hybrid ensemble-based 4D–Var method (En4D-Var) on synthetic data, assessing their estimations of the viscosity and shear modulus of a Kelvin-Voigt material. Results show that En4D–Var and IEnKS provide better moduli estimates than EnKF. Applying these methods to the experimental data of Estrada et al. (2018) yields similar material property estimates to those they obtained, but provides additional information about uncertainties. In particular, the En4D–Var yields lower viscosity estimates for some experiments, and the dynamic estimators reveal a potential mechanism that is unaccounted for in the model, whereby the viscosity is reduced in some cases due to material damage occurring at bubble collapse.

Bryngelson, S. H., Schmidmayer, K., Coralic, V., Maeda, K., Meng, J., & Colonius, T. (2021). MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver. Computer Physics Communications, 266, 107396.

@article{Bryngelson21,
  doi = {10.1016/j.cpc.2020.107396},
  volume = {266},
  year = {2021},
  pages = {107396},
  author = {Bryngelson, S. H. and Schmidmayer, K. and Coralic, V. and Maeda, K. and Meng, J. and Colonius, T.},
  title = {{MFC: A}n open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver},
  journal = {Computer Physics Communications},
  file = {bryngelson-CPC-20.pdf}
}

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock-bubble interaction, and gas bubble cavitation. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock-bubble, shock-droplet, and shock-water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas-liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock-bubble-vessel-wall and acoustic-bubble-net interactions are used to demonstrate the full capabilities of MFC.

2020

Trummler, T., Bryngelson, S. H., Schmidmayer, K., Schmidt, S. J., Colonius, T., & Adams, N. A. (2020). Near-surface dynamics of a gas bubble collapsing above a crevice. Journal of Fluid Mechanics, 899, A16.

@article{trummler19,
  doi = {10.1017/jfm.2020.432},
  title = {Near-surface dynamics of a gas bubble collapsing above a crevice},
  year = {2020},
  volume = {899},
  pages = {A16},
  author = {Trummler, T. and Bryngelson, S. H. and Schmidmayer, K. and Schmidt, S. J. and Colonius, T. and Adams, N. A.},
  journal = {Journal of Fluid Mechanics},
  file = {trummler-JFM-20.pdf}
}

The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order-accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics, and interactions. The wall-pressure distribution associated with erosion potential is a direct consequence of development and intensity of these flow phenomena.

Bryngelson, S. H., Colonius, T., & Fox, R. O. (2020). QBMMlib: A library of quadrature-based moment methods. SoftwareX, 12, 100615.

@article{Bryngelson20,
  author = {Bryngelson, S. H. and Colonius, T. and Fox, R. O.},
  title = {{QBMMlib}: A library of quadrature-based moment methods},
  year = {2020},
  journal = {SoftwareX},
  volume = {12},
  pages = {100615},
  file = {bryngelson-SoftX-20.pdf},
  doi = {10.1016/j.softx.2020.100615}
}

QBMMlib is an open source package of quadrature-based moment methods and their algorithms. Such methods are commonly used to solve fully-coupled disperse flow and combustion problems, though formulating and closing the corresponding governing equations can be complex. QBMMlib aims to make analyzing these techniques simple and more accessible. Its routines use symbolic manipulation to formulate the moment transport equations for a population balance equation and a prescribed dynamical system. However, the resulting moment transport equations are unclosed. QBMMlib trades the moments for a set of quadrature points and weights via an inversion algorithm, of which several are available. Quadratures then closes the moment transport equations. Embedded code snippets show how to use QBMMlib, with the algorithm initialization and solution spanning just 13 total lines of code. Examples are shown and analyzed for linear harmonic oscillator and bubble dynamics problems.

Bryngelson, S. H., Charalampopoulos, A., Sapsis, T. P., & Colonius, T. (2020). A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations. International Journal of Multiphase Flow, 127, 103262.

@article{bryngelson19_ML,
  doi = {10.1016/j.ijmultiphaseflow.2020.103262},
  year = {2020},
  volume = {127},
  pages = {103262},
  author = {Bryngelson, S. H. and Charalampopoulos, A. and Sapsis, T. P. and Colonius, T.},
  title = {A {G}aussian moment method and its augmentation via {LSTM} recurrent neural networks for the statistics of cavitating bubble populations},
  journal = {International Journal of Multiphase Flow},
  file = {bryngelson-IJMF-20.pdf}
}

Phase-averaged dilute bubbly flow models require high-order statistical moments of the bubble population. The method of classes, which directly evolve bins of bubbles in the probability space, are accurate but computationally expensive. Moment-based methods based upon a Gaussian closure present an opportunity to accelerate this approach, particularly when the bubble size distributions are broad (polydisperse). For linear bubble dynamics a Gaussian closure is exact, but for bubbles undergoing large and nonlinear oscillations, it results in a large error from misrepresented higher-order moments. Long short-term memory recurrent neural networks, trained on Monte Carlo truth data, are proposed to improve these model predictions. The networks are used to correct the low-order moment evolution equations and improve prediction of higher-order moments based upon the low-order ones. Results show that the networks can reduce model errors to less than 1 percent of their unaugmented values.

Schmidmayer, K., Bryngelson, S. H., & Colonius, T. (2020). An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics. Journal of Computational Physics, 402, 109080.

@article{schmidmayer19,
  author = {Schmidmayer, K. and Bryngelson, S. H. and Colonius, T.},
  year = {2020},
  volume = {402},
  pages = {109080},
  journal = {Journal of Computational Physics},
  title = {An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics},
  file = {schmidmayer-JCP-20.pdf},
  doi = {10.1016/j.jcp.2019.109080}
}

Numerical simulation of bubble dynamics and cavitation is challenging; even the seemingly simple problem of a collapsing spherical bubble is difficult to compute accurately with a general, three-dimensional, compressible, multicomponent flow solver. Difficulties arise due to both the physical model and the numerical method chosen for its solution. We consider the 5-equation model of Allaire et al. and Massoni et al., the 5-equation model of Kapila et al., and the 6-equation model of Saurel et al. as candidate approaches for spherical bubble dynamics, and both MUSCL and WENO interface-capturing methods are implemented and compared. We demonstrate the inadequacy of the traditional 5-equation model for spherical bubble collapse problems and explain the corresponding advantages of the augmented model of Kapila et al. for representing this phenomenon. Quantitative comparisons between the augmented 5-equation and 6-equation models for three-dimensional bubble collapse problems demonstrate the versatility of the pressure-disequilibrium model. Lastly, the performance of the pressure-disequilibrium model for representing a three-dimensional spherical bubble collapse for different bubble interior/exterior pressure ratios is evaluated for different numerical methods. Pathologies associated with each factor and their origins are identified and discussed.

Bryngelson, S. H., & Colonius, T. (2020). Simulation of humpback whale bubble-net feeding models. Journal of the Acoustical Society of America, 147(2), 1126–1135.

@article{bryngelson19_whales,
  doi = {10.1121/10.0000746},
  year = {2020},
  volume = {147},
  number = {2},
  pages = {1126--1135},
  author = {Bryngelson, S. H. and Colonius, T.},
  title = {Simulation of humpback whale bubble-net feeding models},
  journal = {Journal of the Acoustical Society of America},
  file = {bryngelson-JASA-20.pdf}
}

Humpback whales can generate intricate bubbly regions, called bubble nets, via blowholes. Humpback whales appear to exploit these bubble nets for feeding via loud vocalizations. A fully-coupled phase-averaging approach is used to model the flow, bubble dynamics, and corresponding acoustics. A previously hypothesized waveguiding mechanism is assessed for varying acoustic frequencies and net void fractions. Reflections within the bubbly region result in observable waveguiding for only a small range of flow parameters. A configuration of multiple whales surrounding and vocalizing towards an annular bubble net is also analyzed. For a range of flow parameters, the bubble net keeps its core region substantially quieter than the exterior. This approach appears more viable, though it relies upon the cooperation of multiple whales. A spiral bubble net configuration that circumvents this requirement is also investigated. The acoustic wave behaviors in the spiral interior vary qualitatively with the vocalization frequency and net void fraction. The competing effects of vocalization guiding and acoustic attenuation are quantified. Low void fraction cases allow low-frequency waves to partially escape the spiral region, with the remaining vocalizations still exciting the net interior. Higher void fraction nets appear preferable, guiding even low-frequency vocalizations while still maintaining a quiet net interior.

2019

Bryngelson, S. H., Schmidmayer, K., & Colonius, T. (2019). A quantitative comparison of phase-averaged models for bubbly, cavitating flows. International Journal of Multiphase Flow, 115, 137–143.

@article{bryngelson19_IJMF,
  author = {Bryngelson, S. H. and Schmidmayer, K. and Colonius, T.},
  year = {2019},
  volume = {115},
  pages = {137-143},
  journal = {International Journal of Multiphase Flow},
  title = {A quantitative comparison of phase-averaged models for bubbly, cavitating flows},
  file = {bryngelson-IJMF-19.pdf},
  doi = {10.1016/j.ijmultiphaseflow.2019.03.028}
}

We compare the computational performance of two modeling approaches for the flow of dilute cavitation bubbles in a liquid. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected features, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and field equations for the associated bubble properties are evolved in an Eulerian reference frame. For polydisperse mixtures, the probability density function of the equilibrium bubble radii is discretized and bubble properties are solved for each representative bin. In both cases, the equations are closed by solving Rayleigh–Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. An acoustically excited dilute bubble screen is used as a case study for comparisons. We show that observables of ensemble- and volume-averaged simulations match closely and that their convergence is first order under grid refinement. Guidelines are established for phase-averaged simulations by comparing the computational costs of methods. The primary costs are shown to be associated with stochastic closure; polydisperse ensemble-averaging requires many samples of the underlying PDF and volume-averaging requires repeated, randomized simulations to accurately represent a homogeneous bubble population. The relative sensitivities of these costs to spatial resolution and bubble void fraction are presented.

Bryngelson, S. H., Guéniat, F., & Freund, J. B. (2019). Irregular dynamics of cellular blood flow in a model microvessel. Physical Review E, 100, 012203.

@article{bryngelson19_chaos,
  author = {Bryngelson, S. H. and Gu\'{e}niat, F. and Freund, J. B.},
  volume = {100},
  pages = {012203},
  year = {2019},
  journal = {Physical Review E},
  title = {Irregular dynamics of cellular blood flow in a model microvessel},
  file = {bryngelson-PRE-19.pdf},
  doi = {10.1103/PhysRevE.100.012203}
}

The flow of red blood cells within cylindrical vessels is complex and irregular, so long as the vessel diameter is somewhat larger than the nominal cell size. Long-time-series simulations, in which cells flow 10,000 vessel diameters, are used to characterize the chaotic kinematics, particularly to inform reduced-order models. The simulation model used includes full coupling between the elastic red blood cell membranes and surrounding viscous fluid, providing a faithful representation of the cell-scale dynamics. Results show that the flow has neither classifiable recurrent features nor a dominant frequency. jInstead, its kinematics are sensitive to the initial flow configuration in a way consistent with chaos and Lagrangian turbulence. Phase-space reconstructions show that a low-dimensional attractor does not exist, so the observed long-time dynamics are effectively stochastic. Based on this, a simple Markov chain model for the dynamics is introduced and shown to reproduce the statistics of the cell positions.

Bryngelson, S. H., & Freund, J. B. (2019). Non-modal Floquet stability of a capsule in large amplitude oscillatory extension. European Journal of Mechanics B/Fluids, 77, 171–176.

@article{bryngelson19_LAOE,
  author = {Bryngelson, S. H. and Freund, J. B.},
  volume = {77},
  pages = {171-176},
  year = {2019},
  journal = {European Journal of Mechanics B/Fluids},
  title = {Non-modal {F}loquet stability of a capsule in large amplitude oscillatory extension},
  file = {bryngelson-EJM-19.pdf},
  doi = {10.1016/j.euromechflu.2019.04.012}
}

We analyze the stability of a capsule in large-amplitude oscillatory extensional (LAOE) flow, as often used to study the rheology and dynamics of suspensions. Such a flow is typically established in a cross-slot configuration, with the particle (or particles) of interest observed in the stagnation region. However, controlling this configuration is challenging because the flow is unstable. We quantify such an instability for spherical elastic capsules suspended near the stagnation point using a non-modal global Floquet analysis, which is formulated to include full coupling of the capsule-viscous-flow dynamics. The flow is shown to be transiently, though not asymptotically, unstable. For each case considered, two predominant modes of transient amplification are identified: a predictable intra-period growth for translational capsule perturbations and period-to-period growth for certain capsule distortions. The amplitude of the intra-period growth depends linearly on the flow strength and oscillation period, which corresponds to a shift of the flow stagnation point, and the period-to-period growth saturates over several periods, commensurate with the asymptotic stability of the flow.

2018

Bryngelson, S. H., Pantano, C., Bodony, D., & Freund, J. B. (2018). Adjoint-based sensitivity for flows with shocks. Technical Report, XPACC.

@report{report_1,
  author = {Bryngelson, S. H. and Pantano, C. and Bodony, D. and Freund, J. B.},
  title = {Adjoint-based sensitivity for flows with shocks},
  institution = {Technical Report, XPACC},
  year = {2018},
  file = {bryngelson-xpacc-18.pdf}
}

Developing a consistent solution method for discontinuous adjoint flow problems is challenging. 
The inviscid Burgers’ equation is considered as a step toward the formulation of such a method. Results are shown for linear and nonlinear numerical methods, including WENO shock capturing. Necessary and sufficient conditions for consistent and convergent solutions to the associated adjoint equation are discussed. The adjoint Euler equations are also investigated, for which no numerical schemes are provably convergent. A characteristic-based method for this problem is proposed. It transforms the adjoint equations into an uncoupled set of transport equations. These equations have the same form as the adjoint Burgers’ equation, and thus inherit their proven consistency properties.

Bryngelson, S. H., & Freund, J. B. (2018). Floquet stability analysis of capsules in viscous shear flow. Joural of Fluid Mechanics, 852, 663–677.

@article{bryngelson18_JFM,
  author = {Bryngelson, S. H. and Freund, J. B.},
  journal = {Joural of Fluid Mechanics},
  pages = {663-677},
  title = {Floquet stability analysis of capsules in viscous shear flow},
  volume = {852},
  year = {2018},
  file = {bryngelson-JFM-18.pdf},
  doi = {10.1017/jfm.2018.574}
}

Observations in experiments and simulations show that the kinematic behaviour of an elastic capsule, suspended and rotating in shear flow, depends upon the flow strength, the capsule membrane material properties and its at-rest shape. We develop a linear stability description of the periodically rotating base state of this coupled system, as represented by a boundary integral flow formulation with spherical harmonic basis functions describing the elastic capsule geometry. This yields Floquet multipliers that classify the stability of the capsule motion for elastic capillary numbers Ca ranging from 0.01 to 5. Viscous dissipation rapidly damps most perturbations. However, for all cases, a single component grows or decays slowly, depending upon Ca, over many periods of the rotation. The transitions in this stability behaviour correspond to the different classes of rotating motion observed in previous studies.

Bryngelson, S. H., & Freund, J. B. (2018). Global stability of flowing red blood cell trains. Physical Review Fluids, 3(7), 073101.

@article{bryngelson18_PRF,
  author = {Bryngelson, S. H. and Freund, J. B.},
  journal = {Physical Review Fluids},
  number = {7},
  pages = {073101},
  title = {Global stability of flowing red blood cell trains},
  volume = {3},
  year = {2018},
  file = {bryngelson-PRF-18.pdf},
  doi = {10.1103/PhysRevFluids.3.073101}
}

A train of red blood cells flowing in a round tube will either advect steadily or break down into a complex and irregular flow, depending upon its degree of confinement. We analyze this apparent instability, including full coupling between the viscous fluid flow and the elastic cell membranes. A linear stability analysis is constructed via a complete set of orthogonal perturbations to a boundary integral formulation of the flow equations. Both transiently and asymptotically amplifying disturbances are identified. Those that amplify transiently have short-wavelength shape distortions that carry significant membrane strain energy. In contrast, asymptotic disturbances are primarily rigid-body-like tilts and translations. It is shown that an intermediate cell-cell spacing of about half a tube diameter suppresses long-time train instability, particularly when the vessel diameter is relatively small. Altering the viscosity ratio between the cytosol fluid within the cell and the suspending fluid is found to be asymptotically destabilizing for both higher and lower viscosity ratios. Altering the cytosol volume away from that of a nominally healthy discocyte alters the stability with complex dependence on train density and vessel diameter. Several of the observations are consistent with a switch from predominantly cell-cell interactions for dense trains and predominantly cell-wall interactions for less dense trains. Direct numerical simulations are used to verify the linear stability analysis and track the perturbation growth into a self-sustaining disordered regime.

2017

2016

Bryngelson, S. H., & Freund, J. B. (2016). Buckling and its effect on the confined flow of a model capsule suspension. Rheologica Acta, 55(6), 451–464.

@article{bryngelson16_RA,
  author = {Bryngelson, S. H. and Freund, J. B.},
  journal = {Rheologica Acta},
  number = {6},
  pages = {451-464},
  title = {Buckling and its effect on the confined flow of a model capsule suspension},
  volume = {55},
  year = {2016},
  file = {bryngelson-RA-16.pdf},
  doi = {10.1007/s00397-015-0900-9}
}

The rheology of confined flowing suspensions, such as blood, depends upon the dynamics of the components, which can be particularly rich when they are elastic capsules. Using boundary integral methods, we simulate a two-dimensional model channel through which flows a dense suspension of fluid-filled capsules. A parameter of principal interest is the equilibrium membrane perimeter, parameterized by xi_o, which ranges from round capsules with xi_o=1.0 to xi_o=3.0 capsules with a dog-bone-like equilibrium shape. It is shown that the minimum effective viscosity occurs for xi_o approx 1.6, which forms a biconcave equilibrium shape, similar to a red blood cell. The rheological behavior changes significantly over this range; transitions are linked to specific changes in the capsule dynamics. Most noteworthy is an abrupt change in behavior for xi_o = 2.0, which correlates with the onset of capsule buckling. The buckled capsules have a more varied orientation and make significant rotational (rotlet) contributions to the capsule–capsule interactions.

Bryngelson, S. H., & Freund, J. B. (2016). Capsule-train stability. Physical Review Fluids, 1(3), 033201.

@article{bryngelson16_PRF,
  author = {Bryngelson, S. H. and Freund, J. B.},
  journal = {Physical Review Fluids},
  number = {3},
  pages = {033201},
  title = {Capsule-train stability},
  volume = {1},
  year = {2016},
  file = {bryngelson-PRF-16.pdf},
  doi = {10.1103/PhysRevFluids.1.033201}
}

Elastic capsules flowing in small enough tubes, such as red blood cells in capillaries, are well known to line up into regular single-file trains. The stability of such trains in somewhat wider channels, where this organization is not observed, is studied in a two-dimensional model system that includes full coupling between the viscous flow and suspended capsules. A diverse set of linearly amplifying disturbances, both long-time asymptotic (modal) and transient (nonmodal) perturbations, is identified and analyzed. These have a range of amplification rates and their corresponding forms are wavelike, typically dominated by one of five principal perturbation classes: longitudinal and transverse translations, tilts, and symmetric and asymmetric shape distortions. Finite-amplitude transiently amplifying perturbations are shown to provide a mechanism that can bypass slower asymptotic modal linear growth and precipitate the onset of nonlinear effects. Direct numerical simulations are used to verify the linear analysis and track the subsequent transition of the regular capsule trains into an apparently chaotic flow.