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

TL;DR

This paper introduces a neural network-enhanced pseudo-transient continuation method to improve the convergence of CFD simulations solving Navier-Stokes equations, demonstrating better performance on benchmark problems.

Contribution

The paper presents a novel neural network approach to predict local pseudo-time steps, enhancing the convergence of nonlinear CFD simulations beyond classical methods.

Findings

Neural network predicts local pseudo-time steps effectively.

Improved convergence in benchmark CFD problems.

Enhanced globalization technique for Navier-Stokes simulations.

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.