Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks

• URL: http://arxiv.org/abs/2310.06717v1
• Date: Tue, 10 Oct 2023 15:45:19 GMT
• Title: Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks
• Authors: Anouk Zandbergen, Tycho van Noorden, Alexander Heinlein
• Abstract summary: Navier-Stokes equations may exhibit a highly nonlinear behavior. The system of nonlinear equations resulting from the discretization of the Navier-Stokes equations can be solved using nonlinear iteration methods, such as Newton's method. In this paper, pseudo-transient continuation is employed in order to improve nonlinear convergence.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior. The system of nonlinear equations resulting from the discretization of the Navier-Stokes equations can be solved using nonlinear iteration methods, such as Newton's method. However, fast quadratic convergence is typically only obtained in a local neighborhood of the solution, and for many configurations, the classical Newton iteration does not converge at all. In such cases, so-called globalization techniques may help to improve convergence. In this paper, pseudo-transient continuation is employed in order to improve nonlinear convergence. The classical algorithm is enhanced by a neural network model that is trained to predict a local pseudo-time step. Generalization of the novel approach is facilitated by predicting the local pseudo-time step separately on each element using only local information on a patch of adjacent elements as input. Numerical results for standard benchmark problems, including flow through a backward facing step geometry and Couette flow, show the performance of the machine learning-enhanced globalization approach; as the software for the simulations, the CFD module of COMSOL Multiphysics is employed.

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