Analysis on numerical stability and convergence of Reynolds averaged Navier-Stokes simulations from the perspective of coupling modes

Reynolds-averaged Navier-Stokes (RANS) simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such a situation, machine learning methods provide an effective way to build new data-driven turbulence closure models. Nevertheless, a bottleneck that the data-driven turbulence models encounter is how to ensure the stability and convergence of the RANS equations in a posterior iteration. This paper studies the effects of different coupling modes on the convergence and stability between the RANS equations and turbulence models. Numerical results demonstrate that the frozen coupling mode, commonly used in machine learning turbulence models, may lead to divergence and instability in a posterior iteration; while the mutual coupling mode can maintain good convergence and stability. This research can provide a new perspective to the coupling mode for machine learning turbulence models with RANS equations in a posterior iteration.