Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow
Fabian Pioch,
Jan Hauke Harmening,
Andreas Maximilian Müller,
Franz-Josef Peitzmann,
Dieter Schramm,
Ould el Moctar
Affiliations
Fabian Pioch
Department of Mechanical Engineering, Mechatronics Institute Bocholt, Westphalian University, Münsterstraße 265, 46397 Bocholt, Germany
Jan Hauke Harmening
Department of Mechanical Engineering, Mechatronics Institute Bocholt, Westphalian University, Münsterstraße 265, 46397 Bocholt, Germany
Andreas Maximilian Müller
Department of Mechanical Engineering, Mechatronics Institute Bocholt, Westphalian University, Münsterstraße 265, 46397 Bocholt, Germany
Franz-Josef Peitzmann
Department of Mechanical Engineering, Mechatronics Institute Bocholt, Westphalian University, Münsterstraße 265, 46397 Bocholt, Germany
Dieter Schramm
Department of Mechanical Engineering, University Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany
Ould el Moctar
Department of Mechanical Engineering, Institute for Ship Technology, Ocean Engineering and Transport Systems, University Duisburg-Essen, Bismarckstraße 69, 47057 Duisburg, Germany
Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated the capability of PINNs to solve the Naver–Stokes equations for laminar flows. However, little work has been published concerning the application of PINNs to solve the RANS equations for turbulent flows. This study applied a RANS-based PINN approach to a backward-facing step flow at a Reynolds number of 5100. The standard k-ω model, the mixing length model, an equation-free νt and an equation-free pseudo-Reynolds stress model were applied. The results compared favorably to DNS data when provided with three vertical lines of labeled training data. For five lines of training data, all models predicted the separated shear layer and the associated vortex more accurately.
