@unpublished{zeng22, author = {Zeng, Q. and Bryngelson, S. H. and Sh{\"a}fer, F.}, title = {Competitive physics informed networks}, note = {arXiv: 2204.11144}, file = {zeng-22.pdf}, arxiv = {2204.11144}, year = {2022} }
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.
@unpublished{panchal22, author = {Panchal, A. and Bryngelson, S. H. and Menon, S.}, title = {A seven-equation diffused interface method for resolved multiphase flows}, note = {arXiv: 2204.08637}, file = {panchal-22.pdf}, arxiv = {2204.08637}, year = {2022} }
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.
@unpublished{bryngelson21, author = {Bryngelson, S. H. and Fox, R. O. and Colonius, T.}, title = {Conditional moment methods for polydisperse cavitating flows}, note = {arXiv: 2112.14172}, file = {bryngelson-21.pdf}, arxiv = {2112.14172}, year = {2021} }
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.
@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}, note = {in press [arXiv: 2110.01374]} }
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.
@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.
@article{bryngelson19_CPC, 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.
@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.
@article{bryngelson20_qbmm, 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.
@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.
@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.
@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.
@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.
@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.
@article{bryngelson19_LAOE, author = {Bryngelson, S. H. and Freund, J. B.}, volume = {77}, pages = {171--176}, year = {2019}, journal = {European Journal of Mechanics B}, 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.
@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.
@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.
@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.
@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.
@inproceedings{proceeding_10, author = {Bryngelson, S. H. and Charalampopoulos, A. and Sapsis, T. P. and Fox, R. O. and Colonius, T.}, year = {2022}, title = {Representing statistics of dispersions via moment methods and recurrent neural networks with application to cavitating bubbles}, booktitle = {34rd Symposium on Naval Hydrodynamics}, address = {Washington D.C., USA}, file = {bryngelson-SNH-22.pdf} }
The dynamics of cavitation bubbles are important in many applications, but the wide range of spatio-temporal scales and a large number of bubbles often preclude direct simulations. We develop a statistical Euler–Euler description of sub-grid bubbles that includes, for the first time, the independent variables of the oscillatory cavitation dynamics. The approach stitches together several state-of-the-art computational tools: a generalized population balance representing the statics of the cavitating bubbles, conditional quadrature moment methods (QBMMs) computes them, ensemble phase-averaging couples them to the fluid flow, and high-order-accurate interface capturing stably evolves the flow in time. The one-way-coupled evolution of the forced bubbles is used to evaluate the accuracy of the QBMM statistics against truth data generated through a Monte Carlo approach. CHyQMOM provides the most computationally efficient closure for this purpose, and we implement it in the open-source MFC multiphase flow solver. An acoustically excited bubble screen problem is used to determine the importance and relevance of representing the bubble statistics in this way. Broadening the distribution of bubble radii and radial velocities significantly impacts the dynamics. Broader distributions in radii increase pressure fluctuations, as the averaged bubble oscillations occur at a shorter time scale than the transmitted pressure wave. Broadening the bubble radial velocity distribution results in the opposite effect, smoothing the pressure oscillations observed in the screen region. Our results also show that significant model-form errors can accumulate under strong and long-time pressure forcings. To address this issue, we present a long short-term memory recurrent neural network (LSTM RNN) model that adjusts the quadrature rule to improve its accuracy. The method is tested on a simple one-way-coupled test case and shown to decrease these errors by a factor of about ten. The neural network avoids introducing numerical instabilities by incorporating the moment transport equations and the moment realizability into the loss function.
@inproceedings{proceeding_11, author = {Rodriguez, M. and Bryngelson, S. H. and Colonius, T.}, year = {2022}, title = {Bubble dynamics with phase change near a compliant object}, booktitle = {34rd Symposium on Naval Hydrodynamics}, address = {Washington D.C., USA}, file = {rodriguez-SNH-22.pdf} }
Cavitation near rigid and compliant surfaces leads to damage to naval structures. Phase change is involved in the nucleation, growth, and collapse of bubbles but is often ignored in interface-capturing simulations of multiphase flows. Near-surface bubble collapses and phase change have been studied independently. Still, the importance of phase change during these bubble oscillations and collapses and how this relates to the impact loads at the surface remains unknown. We use the open-source Multi-component Flow Code (MFC), a fully Eulerian framework, to access these scales and model phase change. The Eulerian six-equation multiphase physical and numerical model uses an interface- and shock-capturing approach. Phase change is modeled as a kinetic process involving volume, thermal, and mass transfer at the interface. The numerical implementation is verified using 1D cavitation and shock tube problems and a two-phase relaxation solver with finite relaxation. We then study an underwater explosion cavitation bubble problem near a rigid wall and a rigid wall with an elastomeric coating. The sharp drop of pressure from the rarefaction wave in the wake of the underwater explosion cavitates the liquid near the boundary. We study the dependence of initial bubble stand-off distance from the nearby surface and pressure on the maximum wall pressures and water vapor mass production. The coating inhibits the phase change and reduces the pressure loading experienced at the rigid wall compared to the no-coating case.
@inproceedings{proceeding_8, author = {Rodriguez, M. and Bryngelson, S. H. and Cao, S. and Colonius, T.}, year = {2021}, title = {A unified {E}ulerian multiphase framework for fluid-structure interaction problems including cavitation}, booktitle = {XXV International Congress of Theoretical and Applied Mechanics}, address = {Milano, Italy}, file = {rodriguez-ICTAM-21.pdf} }
Understanding the impact load mechanisms from cavitation bubbles and shocks emitted by their collapse in and near solid deformable media is important for engineering and biomedical applications. In such flows, transient pressure fluctuations can lead toa cloud of small vapor bubbles near the solid object. A unified Eulerian framework for fluid-structure interaction problems includingcavitation is developed to incorporate numerically unresolved and resolved bubbles and the solid material elasticity. The numericalmodel uses interface-capturing techniques for the fluid-structure coupling with phase change. The method is based on a high-orderaccurate weighted essentially non-oscillatory shock and interface capturing scheme. Studies of single bubble and cloud dynamics neara solid/compliant structure relevant to therapeutic ultrasound applications are presented.
@inproceedings{proceeding_1, author = {Spratt, J.-S. and Rodriguez, M. and Bryngelson, S. H. and Cao, S. and Colonius, T.}, title = {Eulerian framework for bubble-cloud-kidney stone interaction}, booktitle = {11th International Symposium on Cavitation}, year = {2021}, address = {Daejeon, Korea}, file = {spratt-CAV-21.pdf} }
Burst-wave lithotripsy (BWL) is a therapy for ablating kidney and gall bladder stones. During therapy, high-amplitude ultrasound waves issue from a transducer array and focus near the stone. These waves can nucleate clouds of small bubbles at the surface of the stone. This can affect treatment efficacy: acoustic shielding due to the bubble clouds can attenuate stone breakup, though the collapse of individual bubbles can amplify it. Further, these collapses can cause damage to surrounding tissue. Thus, optimizing lithotripsy against potential damage requires predicting bubble-stone interactions. Simulating bubble cloud cavitation is challenging due to the breadth of spatio-temporal scales involved. Additional scale restrictions are associated with soft material dynamics, which interact with the bubble clouds during lithotripsy. The open-source solver MFC can address these challenges. It uses a phase-averaging sub-grid model for bubble cloud cavitation and has been extended to include a hypoelastic Kelvin–Voigt model to compute stresses in stones and nearby soft surfaces. These models are fully-coupled to the fluid dynamics. The capabilities of this approach are demonstrated for a model BWL problem. The stress state in a kidney stone is modeled during treatment.
@inproceedings{proceeding_9, author = {Bryngelson, S. H. and Colonius, T.}, year = {2021}, title = {Closure of phase-averaged bubbly, cavitating flow models}, booktitle = {XXV International Congress of Theoretical and Applied Mechanics}, address = {Milano, Italy}, file = {bryngelson-ICTAM-21.pdf}, url = {https://vimeo.com/640932583/0ae772bf00} }
Phase-averaged bubbly flow models are closed by high-order statistical moments of the disperse bubble dynamics. Evaluating these moments in a simulation environment is computationally expensive because the integrands are highly oscillatory. The cost of this closure is demonstrated for an ensemble-averaged bubbly flow model. A machine-learning-based method for accelerating the moment evaluation is formulated.
@inproceedings{proceeding_3, author = {Bryngelson, S. H. and O'Meally, F. and Colonius, T. and Fox, R. O.}, title = {Conditional moment method for fully-coupled phase-averaged cavitation models}, booktitle = {11th International Symposium on Cavitation}, year = {2021}, address = {Daejeon, Korea}, file = {bryngelson-CAV-21.pdf}, url = {https://vimeo.com/640931949/a6cd12fc05} }
Eulerian sub-grid models for the bubble dynamics associated with cavitation are an increasingly viable route for simulating engineering-scale bubbly flow problems. We identify two primary concerns towards enabling physically faithful simulations: sub-grid model fidelity and computational cost. Previous Euler–Euler models considered the sub-grid bubble radius and radial velocity to be deterministic functions of the bubble dynamics model and pressure forcing. We relax this assumption, allowing the bubble radii and radial velocities to be arbitrary probability density functions conditioned on the equilibrium bubble size. Conditional moment inversion methods reconstruct quadrature nodes and weights in the internal coordinate directions, which are then used to compute the moments that close the fully coupled flow equations. A one-dimensional acoustically excited bubble screen is used to study the resulting models. Computationally, resolving radius and radial velocity variations requires only a modest additional cost when compared to that of the R_o-coordinate, which has a highly oscillatory behavior. The observed bubble screen pressures show that variation of the bubble probability density functions lead to variations in the dynamic response of the bubble screen. For example, we observe an increase in pressure fluctuations with increasing radial variation, as the bubbles oscillate at shorter time scales than the transmitted acoustic wave, while increasing velocity variation reduces the observed pressure fluctuations. Thus, modeling the instantaneous radius and velocity distributions is necessary if actual cavitating bubble clouds are in such statistical disequilibria.
@inproceedings{proceeding_2, author = {Rodriguez, M. and Bryngelson, S. H. and Cao, S. and Colonius, T.}, title = {Acoustically-induced bubble growth and phase change dynamics near compliant surfaces}, booktitle = {11th International Symposium on Cavitation}, year = {2021}, address = {Daejeon, Korea}, file = {rodriguez-CAV-21.pdf} }
Biomedical therapies use focused ultrasound to treat pathogenic tissues. The ultrasound waves lead to nucleation, grow and collapse of bubbles. Previous numerical simulations of this process have treated the bubble contents as non-condensible gas, but it is known that phase change affects the bubble dynamics as a function of the driving frequency and waveform. In this study, we incorporate phase change in the six-equation, multiphase model previously implemented in our Multi-component Flow Code (MFC). The implementation is verified with 1D cavitation and shock problems. To highlight the effects of phase change, we simulate the expansion of a 2D bubble near a solid, rigid boundary to observe phase change near the interface.
@inproceedings{proceeding_7, author = {Bryngelson, S. H. and Colonius, T.}, year = {2020}, title = {Phase- and mixture-averaged techniques for general bubbly flows}, booktitle = {33rd Symposium on Naval Hydrodynamics}, address = {Osaka, Japan}, file = {bryngelson-SNH-20.pdf}, url = {https://vimeo.com/640930931/6e57ccfd89} }
Averaged models are used to represent cavitating bubbly mixtures at the sub-grid computational level. Though such averaging techniques are widely used, the relative computational performance of various adaptations remains unknown. The accuracy and computational efficiency of two such models, one ensemble-averaging and one volume-averaging, addresses this issue. Results show that the relative computational cost of the methods depends upon the degree of bubble polydispersity. The ensemble-averaged model requires more quadrature nodes for broader population sizes and increasingly broad populations become computationally untenable. A moment-based method addresses this shortcoming. It uses a Gaussian closure and is augmented via long short-term memory recurrent neural networks for high-order statistics. Results show that this approach achieves small relative errors for even high-order statistical moments using only five degrees of freedom, significantly fewer than the hundreds required by classes methods.
@inproceedings{proceeding_6, title = {A comparison of ensemble- and volume-averaged bubbly flow models}, author = {Bryngelson, S. H. and Colonius, T.}, booktitle = {10th International Conference on Multiphase Flow}, address = {Rio de Janeiro, Brazil}, year = {2019}, file = {bryngelson-ICMF-19.pdf} }
We compare volume- and ensemble-averaged bubbly flow models. Volume-averaging is a deterministic process for which bubbles are represented in a Lagrangian framework as advected particles, each sampled from a distribution of equilibrium bubble sizes. Ensemble-averaging instead uses mixture-averaged equations in an Eulerian reference frame for the associated bubble properties, each represented by bins of the equilibrium distribution. In both cases, bubbles are modeled as spherical with dynamics governed by the Keller-Miksis equation. Computationally, there are tradeoffs between these two approaches. Here, we simulate an acoustically excited dilute bubble screen and compare the computational efficiency of the two approaches.
@inproceedings{proceeding_4, title = {Buckling and the rheology of an elastic capsule suspension}, author = {Bryngelson, S. H. and Freund, J. B.}, booktitle = {XXIV International Congress of Theoretical and Applied Mechanics}, address = {Montreal, Canada}, year = {2016}, file = {bryngelson-ICTAM-16.pdf} }
The rheological behavior of an elastic capsule suspension is studied in a model two-dimensional channel using detailed numerical simulations. As the rest capsule membrane aspect ratio increases, the capsules become increasingly vulnerable to a buckling instability. This buckling behavior is concomitant with a sudden increase in the effective viscosity and a near disappearance of any near-wall capsule-free layer. The microstructure dynamics suggest elongated capsules make significant rotational contributions that disrupt organized flow, as computed by their rotlet capsule-capsule interactions.
@inproceedings{proceeding_5, title = {The stability of flowing trains of confined red blood cells}, author = {Freund, J. B. and Bryngelson, S. H.}, booktitle = {XXIV International Congress of Theoretical and Applied Mechanics}, address = {Montreal, Canada}, year = {2016}, file = {freund-ICTAM-16.pdf} }
The asymptotic and transient stability of single-file trains of fluid-filled elastic capsules flowing in narrow channels is analyzed as a model for the lines of red blood cells commonly observed in small tubes or vessels. The most amplified disturbances in larger channels are found to have a rich variety of characteristics depending upon the details of the particular configuration. Transient growth mechanisms are found to be significant, even for relatively small perturbations, and are shown to precipitate nonlinear saturation and chaotic flow many times more quickly than the asymptotic stability would predict even for nominally small perturbations.
@report{bryngelson_xpacc, 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.
@thesis{bryngelson_thesis, author = {Bryngelson, S. H.}, title = {Stability and transition of capsule-flow systems}, year = {2017}, school = {University of Illinois at Urbana--Champaign}, note = {Ph.D. Thesis}, file = {bryngelson-dissertation-17.pdf} }
This work focuses on the mechanical stability of three different capsule-viscous-flow-systems. Red blood cells, which are often modeled as capsules, can form uniform trains when flowing in narrow confines; however, in less confined environments their flow appears disordered. This time-stationary system is analyzed through a nonmodal stability analysis which includes full coupling between the viscous fluid flow and elastic cell membranes. The linearization is constructed via a complex set of orthogonal small disturbances which are evaluated using boundary integral techniques. Transiently (t -> 0+) and asymptotically (t -> infty) unstable disturbances are identified, with their corresponding growth rates and perturbation conformations depending upon on the flow strength, viscosity ratio between the inner and exterior cell fluids, cell–cell spacing, cell at-rest shape, and vessel diameter. An ellipsoidal capsule subject to homogeneous shear flow is also considered. While this flow configuration is seemingly more simple, the base motion of the capsule is time-dependent, though periodic, rather than steady, requiring an extension of our methods. This capsule flow is known to display different kinematic behavior, depending on the flow strength, membrane material properties, and capsule shape. The stability of the capsule motion has been studied based on empirical observations of simulations; here we build upon these results though a direct stability analysis. Our analysis utilizes Floquet methods, which yields Floquet multipliers that classify the asymptotic stability of the capsule motion, and quantify how viscous dissipation will rapidly damp most disturbances. However, we also identify disturbances that decay slowly, over many periods of the capsules rotating motion, as well as neutrally stable perturbations. The last flow system considered here is a spherical capsule subject to large amplitude oscillatory extensional (LAOE) flow, which is often used to study the rheology and dynamics of complex fluids. Examining soft particles in LAOE is particularly challenging, partially due to the instability of the flow system. We again quantify this stability through linear analysis, here extending the aforementioned Floquet formulation to include nonmodal and intra-period effects. The analysis shows the asymptotic stability of the capsules for all flow descriptions, as defined by the relative flow strength and capsule time scale. Transiently unstable modes are found for all cases, though again their growth saturates quickly. We also identify an intra-period instability to capsule translations, which matches that of a rigid particle, though it does not have finite amplification from period-to-period.
Last updated on May 17, 2022
© 2019-2022 Computational Physics @ GT CSE