Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session T24: Computational Fluid Dynamics: Algorithms II; Shock Capturing; SPH & Mesh Free Methods |
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Chair: Michael Chertkov, University of Arizona Room: North 224 B |
Tuesday, November 23, 2021 12:40PM - 12:53PM |
T24.00001: Eulerian simulation of complex suspensions and biolocomotion in three dimensions Yuexia L Lin, Nicholas J Derr, Christopher Rycroft We present a numerical method specifically designed for simulating three-dimensional fluid–structure interaction (FSI) problems based on the reference map technique (RMT). The RMT is a fully Eulerian FSI numerical method that allows fluids and large-deformation elastic solids to be represented on a single fixed computational grid. This eliminates the need for meshing complex geometries typical in other FSI approaches, and greatly simplifies the coupling between fluid and solids. We develop a three-dimensional implementation of the RMT, parallelized using the distributed memory paradigm, to simulate incompressible FSI with neo-Hookean solids. As part of our method, we develop a new field extrapolation scheme that works efficiently in parallel. Through representative examples, we demonstrate the method's suitability in investigating many-body and active systems. |
Tuesday, November 23, 2021 12:53PM - 1:06PM |
T24.00002: Made for each other: adjoint solvers and high-dimensional gradient-augmented Bayesian optimization Ushnish Sengupta, Yubiao Sun, Matthew P Juniper Bayesian optimization (BO) is a global optimization algorithm well-suited for multimodal functions that are costly to evaluate, e.g. quantities derived from computationally expensive simulations. Recent studies have shown that it is possible to scale Bayesian optimization to high-dimensional functions and that its convergence can be accelerated by incorporating derivative information. These developments have laid the groundwork for a productive interplay between Bayesian optimization and adjoint solvers, a tool to cheaply obtain gradients of objective functions w.r.t. tunable parameters in a simulated physical system. Gradient-enhanced high dimensional BO can explore a design space efficiently without getting stuck in local minima. We demonstrate the application of this algorithm to two test cases. The first one is the classic problem of 2D airfoil shape optimization to maximize the lift-to-drag ratio. The second test case uses solutions from an adjoint Helmholtz solver to stabilize a thermoacoustically unstable combustor with geometry changes. We show that compared to L-BFGS, a standard quasi-Newton method, the gradient-enhanced high dimensional BO arrives at multiple, more optimal geometries using considerably fewer evaluations of the solver. |
Tuesday, November 23, 2021 1:06PM - 1:19PM |
T24.00003: Construction of stable difference schemes using a generative model Nek Sharan, Mahesh Natarajan, Peter T Brady, Daniel Livescu High-fidelity turbulent flow simulations require long-time calculations with non-dissipative schemes to accurately determine high-order flow statistics. Stable boundary treatments are key to these calculations over non-trivial domains. This study applies controllable generation using a novel neural-network-based generative model to derive stable boundary stencils for high-order finite-difference schemes. Generative models have been widely used for image generation. They learn the non-linear mapping from a latent distribution to the real data and, given an input noise, generate images of a certain class. Selective manipulation of the input, called controllable generation, then allows change in target attributes, e.g. age or hair color in facial images, while preserving other image features. The generative approach to map a random distribution to stable boundary stencil coefficients is applied in two steps. In the first step, the weights & biases of a neural network (NN) are determined to minimize a cost function comprised of the unstable eigenvalues of the Lyapunov operator for the system matrix. In the second step, the NN weights & biases are fixed and the input is modified to obtain stable stencil coefficients. The efficacy of the approach is demonstrated for various problems. |
Tuesday, November 23, 2021 1:19PM - 1:32PM |
T24.00004: Three-dimensional realizations of the flood flow field in large-scale rivers using convolutional neural networks Zexia Zhang, Ali Khosronejad We present a systematic study to develop autoencoder convolutional neural networks (CNNs) to predict statistical properties of turbulent flood flow of large-scale rivers with several bridge foundations. The training dataset to develop CNN algorithms is obtained from high-fidelity numerical simulation of the flood flow using large-eddy simulation (LES). The developed CNN algorithms are shown to predict the first- and second-order turbulent statistics of the turbulent flood flow at a small fraction of the computational cost of the high-fidelity simulations. The CNN predictions are validated using separately done LES results of different meandering large-scale river. The results show good agreement between the LES and CNN algorithms marking the promise of such artificial intelligent systems to produce efficient flood flow field in large-scale rivers. |
Tuesday, November 23, 2021 1:32PM - 1:45PM |
T24.00005: Simulating shocks and discontinuities by solving the spatially-filtered Euler equations Alexandra Baumgart, Guillaume Blanquart To ensure numerical stability in the vicinity of shocks, a variety of methods have been used. These methods include shock capturing schemes such as weighted essentially non-oscillatory (WENO) schemes, as well as the addition of artificial diffusivities to the governing equations. Centered finite difference schemes are often avoided near discontinuities due to the tendency for significant oscillations. However, such schemes have desirable conservation properties compared to many shock-capturing schemes. The objective of this work is to perform accurate and stable simulations of discontinuities by deriving diffusion terms from first principle and then applying these analytical terms within a centered differencing framework. The physical Euler equations are filtered, and a sub-filter scale term for the momentum equation is extracted specifically for a shock. No sub-filter scale terms are required for the continuity, energy, or species equations. Rather, there is a minimum amount of numerical diffusion required for the energy and species equations. This approach is tested for a variety of problems involving shocks and discontinuities. |
Tuesday, November 23, 2021 1:45PM - 1:58PM Not Participating |
T24.00006: Approximating an artificial viscosity operator with neural networks in a shock-capturing scheme Aaron Larsen, Britton Olson An alternative method for computing artificial viscosity (AV) for shock-capturing is proposed and evaluated on a collection of test problems where shock or discontinuities are present. An artificial neural network (NN) is trained and applied on shock-dominated numerical test problems and used as a means of approximating the AV operator. We present a method to formulate an artificial neural network that predicts artificial viscosity (NN-AV) values using simulation data as the input parameters. This NN-AV is then used to numerically diffuse the shocks in the simulation and the results are compared using the standard AV operator. The artificial neural network is created using standard practices and the TensorFlow library through the collection and training of an input dataset from canonical shock-dominated problems. A simple proof of concept of the NN-AV framework is demonstrated on the viscous Burgers' equation. The model is extended to the Euler equations in both one- and two-dimensions. The accuracy of this trained model is then assessed on other test problems. The accuracy of the results relative to the standard AV operator is evaluated and summarized for all test problems. The order of accuracy for smooth problems and the potential runtime savings from using this new model are discussed. |
Tuesday, November 23, 2021 1:58PM - 2:11PM |
T24.00007: A consistent artificial diffusivity model for capturing discontinuities in compressible flows using central spatial discretization Shahab Mirjalili, Soren Taverniers, Henry Collis, Ali Mani We present a novel computational model for simulation of compressible flows involving shocks and contact discontinuities using an artificial diffusivity approach. Owing to their non-dissipative nature and secondary conservation properties, second order central operators have been shown to be very accurate for simulation of turbulent flows and acoustics. Committing to second order central spatial operations, we control their large dispersion errors by augmenting the mass, momentum and total energy equations with artificial mass diffusivity, artificial shear/bulk viscosities and artificial thermal conductivity, respectively. We show that the presence of artificial mass diffusivity must be consistently accounted for by additional terms in the momentum and total energy equations and compatibility conditions must be met when discretely computing these terms. Next, unlike previous phenomenological localization strategies, inspired by analysis of second order TVD schemes, we present a novel approach for localizing the artificial diffusivity terms. The performance of our proposed computational model is first assessed using canonical 1D tests. Finally, we present simulation results from realistic problems involving shock-boundary layer interactions in a compression corner geometry. |
Tuesday, November 23, 2021 2:11PM - 2:24PM |
T24.00008: Physics Informed Machine Learning of Smooth Particle Hydrodynamics: Validation of the Lagrangian Turbulence Approach Michael Woodward, Yifeng Tian, Michael Chertkov, Mikhail Stepanov, Daniel Livescu, Criston M Hyett, Chris Fryer Smooth particle hydrodynamics (SPH) is a mesh-free Lagrangian method for obtaining approximate numerical solutions of the equations of fluid dynamics, which has been widely applied to weakly- and strongly compressible turbulence in astrophysics and engineering applications. In this work, we develop a hierarchy of parameterized and learn-able SPH simulators, by mixing automatic differentiation (both forward and reverse mode) with forward and adjoint based sensitivity analyses. We show that our physics inspired learning method is capable of: (a) solving inverse problems over both the physically interperatable parameter space, as well as over the space of Neural Network functions; (b) learning Lagrangian statistics of turbulence; (c) combining trajectory based, probabilistic, and field based loss functions; and (d) extrapolating beyond training sets into more complex regimes of interest. |
Tuesday, November 23, 2021 2:24PM - 2:37PM |
T24.00009: A Multi-Block Neural Networks for General and Approximate Riemann problems. Huangsheng Wei, Zhu Huang, Guang Xi The Riemann solver plays very important role on shock capturing method in computational fluid dynamics. Although significant breakthroughs have been conducted in the study of Riemann problems, only one-dimensional standard Riemann problem could be solved analytically. In this study, we proposed Multi-Block Neural Networks (MBNNs) to approximate the exact solution of general Riemann problem, based on the Physically Informed Neural Networks (PINNs) and the Shock Position Neural Networks (SPNNs). |
Tuesday, November 23, 2021 2:37PM - 2:50PM |
T24.00010: Vortex breakdown in non-isothermal gaseous swirling jets Ben Keeton, Jaime Carpio, Keiko K Nomura, Antonio L Sanchez, Forman A Williams Numerical simulations are performed to study vortex breakdown in low-Mach-number swirling jets at moderate Reynolds numbers with thermal effects. The jet-to-ambient density ratio Λ is varied from 1/5 to 5, with the temperature dependence of the gas density and viscosity as that of air. An effective Reynolds number, Reeff, is defined based on the geometric mean of the jet and ambient fluid viscosities. As observed in constant density jets (Billant et al. 1998), two basic types of vortex breakdown are observed: the bubble and the cone configurations. A series of axisymmetric flow simulations at fixed Reeff was used to determine the critical swirl number S for the onset of the bubble (S*B) and the cone (S*C), and results are compared with theoretical predictions. Values of S*B decrease monotonically as Λ increases due to an increased expansion of the flow. Values of S*C depend strongly on viscous effects. For small values of Λ, the low jet Reynolds number delays the transition to the cone while for large values of Λ, the large increase in ambient kinematic viscosity produces a corresponding trend that significantly increases S*C. Results from three-dimensional simulations provide details of the structure and behavior of these flows. |
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