ECCOMAS 2024

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

  • Zandbergen, Anouk (Technische Universität Berlin)
  • Heinlein, Alexander (Delft University of Technology)
  • van Noorden, Tycho (COMSOL BV)

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Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. The Navier-Stokes equations may exhibit a highly nonlinear behavior, depending on the Reynolds number. Discretization of the Navier-Stokes equations leads to a system of nonlinear equations, which can be solved using nonlinear iteration methods, such as Newton’s method. However, to obtain fast quadratic convergence, the Newton iteration must be close enough to the root. Resulting that, for many configurations, the classical Newton iteration does not converge at all, and so-called globalization techniques may help to improve convergence. In this talk, pseudo-time stepping is employed as a globalization technique to improve convergence for the stationary Navier-Stokes equations. The classical algorithm is enhanced by a neural network model trained to predict the local pseudo-time step. To facilitate generalization, the pseudo-time step will be predicted on element level using local information on a patch of adjacent elements as input for the network. Numerical results for standard benchmark problems, including flow through a backward facing step (BFS) geometry and Couette flow, are presented to show the performance of the machine learning-enhanced globalization technique; as the software for the simulations, we employ the CFD module of COMSOL Multiphysics.