Robust turbulent flow simulations using a Reynolds-stress-transport model on unstructured grids

• Design of an unconditionally stable scheme for RSTM on unstructured grids.
• Second-order accuracy is employed for the Reynolds stress model equations.
• The limiter used for the RSTM has a key role in the convergence characteristics.
• The diffusive and convective fluxes of the RSTM require a careful numerical treatment.

Progress toward a stable and efficient numerical treatment for the Reynolds-averaged Navier–Stokes equations with a Reynolds-stress-transport model on unstructured grids is presented. The unconditionally stable time marching scheme for Reynolds-stress-transport models, originally developed by the author for structured grids, is extended for unstructured grids using a finite volume method. The scheme guarantees the convergence of the fixed point iteration on the linearized problem. Moreover, the scheme is a positivity-preserving scheme, regardless of the time step. Thanks to the scheme characteristics, a spatially second-order discretization method for the Reynolds stress model equations (exactly as applied to the mean-flow equations) can be used, free of stability difficulties within the fixed point iterations. It is shown that the limiter has a dramatic influence on the convergence characteristics. Specifically, the limiter applied to the turbulence model variables was found to significantly influence the overall convergence behavior. Another key to the overall flow solver stability is a simple and robust procedure that is proposed to explicitly enforce all the realizability conditions of the Reynolds stress tensor. Two- and three-dimensional numerical flow simulations demonstrate the robustness of the overall flow solver for industrial applications.