A data-driven physics-informed finite-volume scheme for nonclassical undercompressive shocks

Bezgin, Deniz A.; Schmidt, Steffen J.; Adams, Nikolaus A.

doi:10.1016/j.jcp.2021.110324

Cited by 22 publications

(7 citation statements)

References 36 publications

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“…The semi-minor b e for each individual sample is computed by drawing an aspect ratio a e /b e ∈ [2,4] from a random uniform distribution.…”

Section: Data Generation and Datasetsmentioning

confidence: 99%

“…We train multilayer perceptrons to predict the curvature, similar to what is presented for the volume fraction and apertures (compare section 2). From experience, we have seen that to achieve a predictive ] and an aspect ratio [2,4].…”

Section: Appendix a Model Trainingmentioning

confidence: 99%

“…Recently, machine learning methods have been used to substitute certain parts of conventional computational fluid dynamics solvers. Examples are cell-face reconstruction in finite-volume solvers [4] and the curvature computation in VOF [5,6] and Smoothed-particle hydrodynamic [7] codes. The general procedure can be described as follows: ML models are trained separately from the solver in a supervised fashion on a dataset generated by generic, circular interface configurations.…”

Section: Introductionmentioning

confidence: 99%

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Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

Buhendwa,

Bezgin,

Adams

2021

Preprint

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Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers or the curvature computation in the Volume-of-Fluid (VOF) method. The latter showed improvements in terms of accuracy for coarsely resolved interfaces, however at the expense of convergence and symmetry. In this work, a combined approach is proposed, adressing the aforementioned shortcomings. We focus on interface reconstruction (IR) in the level-set method, i.e. the computation of the volume fraction and apertures. The combined model consists of a classification neural network, that chooses between the conventional (linear) IR and the neural network IR depending on the local interface resolution. The proposed approach improves accuracy for coarsely resolved interfaces and recovers the conventional IR for high resolutions, yielding first order overall convergence. Symmetry is preserved by mirroring and rotating the input level-set grid and subsequently averaging the predictions. The combined model is implemented into a CFD solver and demonstrated for two-phase flows. Furthermore, we provide details of floating point symmetric implementation and computational efficiency.

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“…The semi-minor b e for each individual sample is computed by drawing an aspect ratio a e /b e ∈ [2,4] from a random uniform distribution.…”

Section: Data Generation and Datasetsmentioning

confidence: 99%

Section: Appendix a Model Trainingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

Buhendwa,

Bezgin,

Adams

2021

Preprint

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“…Apart from PINNs, the other frameworks which employed deep neural networks for tackling shock wave problems can be found in [24,25,26,27,28]. Inverse problems in supersonic compressible flows are often encountered in designing specialized high-speed vehicles.…”

Section: Introductionmentioning

confidence: 99%

Physics-informed neural networks for inverse problems in supersonic flows

Jagtap,

Mao,

Adams

et al. 2022

Preprint

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Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren photography as well as data at the inflow and part of wall boundaries. These inverse problems are notoriously difficult and traditional methods may not be adequate to solve such ill-posed inverse problems. To this end, we employ the physics-informed neural networks (PINNs) and its extended version, extended PINNs (XPINNs), where domain decomposition allows to deploy locally powerful neural networks in each subdomain, which can provide additional expressivity in subdomains, where a complex solution is expected. Apart from the governing compressible Euler equations, we also enforce the entropy conditions in order to obtain viscosity solutions. Moreover, we enforce positivity conditions on density and pressure. We consider inverse problems involving two-dimensional expansion waves, two-dimensional oblique and bow shock waves. We compare solutions obtained by PINNs and XPINNs and invoke some theoretical results that can be used to decide on the generalization errors of the two methods.

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“…In [40], a differentiable solver was placed in the training loop to reduce the error of iterative solvers. Bezgin et al [41] have put forward a subgrid scale model for nonclassical shocks. Kochkov et al.…”

Section: Introductionmentioning

confidence: 99%

JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows

Bezgin¹,

Buhendwa²,

Adams³

2022

Preprint

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Physical systems are governed by partial differential equations (PDEs). The Navier-Stokes equations describe fluid flows and are representative of nonlinear physical systems with complex spatio-temporal interactions. Fluid flows are omnipresent in nature and engineering applications, and their accurate simulation is essential for providing insights into these processes. While PDEs are typically solved with numerical methods, the recent success of machine learning (ML) has shown that ML methods can provide novel avenues of finding solutions to PDEs. ML is becoming more and more present in computational fluid dynamics (CFD). However, up to this date, there does not exist a generalpurpose ML-CFD package which provides 1) powerful state-of-the-art numerical methods, 2) seamless hybridization of ML with CFD, and 3) automatic differentiation (AD) capabilities. AD in particular is essential to ML-CFD research as it provides gradient information and enables optimization of preexisting and novel CFD models. In this work, we propose JAX-FLUIDS: a comprehensive fullydifferentiable CFD Python solver for compressible two-phase flows. JAX-FLUIDS allows the simulation of complex fluid dynamics with phenomena like three-dimensional turbulence, compressibility effects, and two-phase flows. Written entirely in JAX, it is straightforward to include existing ML models into the proposed framework. Furthermore, JAX-FLUIDS enables end-to-end optimization. I.e., ML models can be optimized with gradients that are backpropagated through the entire CFD algorithm, and therefore contain not only information of the underlying PDE but also of the applied numerical methods. We believe that a Python package like JAX-FLUIDS is crucial to facilitate research at the intersection of ML and CFD and may pave the way for an era of differentiable fluid dynamics.

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A data-driven physics-informed finite-volume scheme for nonclassical undercompressive shocks

Cited by 22 publications

References 36 publications

Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

Physics-informed neural networks for inverse problems in supersonic flows

JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows

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