Improving Pseudo-time Stepping Convergence for CFD Simulations with Neural Networks

Strategic Insights -

Recent research published in Computers & Mathematics with Applications has shed light on a novel approach to improving pseudo-time stepping convergence for computational fluid dynamics (CFD) simulations. The study, led by Alexander Heinlein from the Delft University of Technology, employed a neural network model to predict a local pseudo-time step, thereby enhancing the classical algorithm for nonlinear convergence. The research team, which also includes Anouk Zandbergen and Tycho van Noorden, demonstrated the performance of the machine learning-enhanced globalization approach on standard benchmark problems, including flow over a backward facing step geometry and Couette flow.

Key Takeaways:

  • The research focused on improving pseudo-time stepping convergence for CFD simulations of viscous fluids described by the stationary Navier-Stokes equations.
  • The study employed a neural network model to predict a local pseudo-time step, enhancing the classical algorithm for nonlinear convergence.
  • The machine learning-enhanced globalization approach was demonstrated on standard benchmark problems, including flow over a backward facing step geometry and Couette flow.
  • The research used the CFD Module of COMSOL Multiphysics software for simulations and achieved quadratic convergence for a wide range of Reynolds numbers.
  • The application of a neural network model facilitated the generalization of the novel approach by predicting the local pseudo-time step separately on each element using only local information.
  • The research has been peer-reviewed and published in Computers & Mathematics with Applications, a reputable journal in the field.

Statistics:

  • The research was published in Computers & Mathematics with Applications in 2025 (Vol. 196, pp. 64-83).
  • The study employed the CFD Module of COMSOL Multiphysics software for simulations.
  • The research achieved quadratic convergence for a wide range of Reynolds numbers (10^-3 to 10^6).
  • The application of a neural network model facilitated the prediction of a local pseudo-time step on each element, using only local information.
  • The research demonstrated the performance of the machine learning-enhanced globalization approach on standard benchmark problems, including flow over a backward facing step geometry and Couette flow.

Sources:

  • Heinlein, A., Zandbergen, A., & van Noorden, T. (2025). Improving Pseudo-time Stepping Convergence for Cfd Simulations With Neural Networks. Computers & Mathematics with Applications, 196, 64-83.
  • Delft University of Technology. (2025). Improving Pseudo-time Stepping Convergence for Cfd Simulations With Neural Networks. Journal of Engineering. October 20, 2025; p 2791.
  • Pergamon-elsevier Science Ltd. (2025). Computers & Mathematics with Applications. The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, England.