A robust implicit multigrid method for RANS equations with two-equation turbulence models

作者：Wasserman M; Mor Yossef Y^*; Yavneh I; Greenberg J B

来源：Journal of Computational Physics, 2010, 229(16): 5820-5842.

DOI：10.1016/j.jcp.2010.04.023

• RANS
• Turbulence model
• Positivity preservation
• Numerical stiffness
• Source term
• Multigrid

The design of a new, truly robust multigrid framework for the solution of steady-state Reynolds-Averaged Navier-Stokes (RANS) equations with two-equation turbulence models is presented. While the mean-flow equations and the turbulence model equations are advanced in time in a loosely-coupled manner, their multigrid cycling is strongly coupled (FC-MG). Thanks to the loosely-coupled approach, the unconditionally positive-convergent implicit time-integration scheme for two-equation turbulence models (UPC) is used. An improvement to the basic UPC scheme convergence characteristics is developed and its extension within the multigrid method is proposed. The resulting novel FC-MG-UPC algorithm is nearly free of artificial stabilizing techniques, leading to increased multigrid efficiency. To demonstrate the robustness of the proposed algorithm, it is applied to linear and non-linear two-equation turbulence models. Numerical experiments are conducted, simulating separated flow about the NACA4412 airfoil, transonic flow about the RAE2822 airfoil and internal flow through a plane asymmetric diffuser. Results obtained from numerical simulations demonstrate the strong consistency and case-independence of the method.