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Reynolds-averaged Navier-Stokes simulations are still the main method tostudy complex flows in engineering. However, traditional turbulence modelscannot accurately predict flow fields with separations. In such situation,machine learning methods provide an effective way to build new data-driventurbulence closure models. Nevertheless, a bottleneck that the data-driventurbulence models encounter is how to ensure the stability and convergence ofthe RANS equations in posterior iterations. This paper studies the effects ofdifferent coupling modes on the convergence and stability between the RANSequations and turbulence models. Numerical results demonstrate that the frozencoupling mode, commonly used in machine learning turbulence models, may lead todivergence and instability in posterior iterations; while the mutual couplingmode can maintain good convergence and stability in the process of iterations.This research can provide a new perspective to the coupling mode for machinelearning turbulence models with RANS equations in posterior iterations.

Analysis on numerical stability and convergence of RANS turbulence models from the perspective of coupling modes