A robust implicit multigrid method for RANS equations with two-equation turbulence models |
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Authors: | M. Wasserman Y. Mor-Yossef I. Yavneh J.B. Greenberg |
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Affiliation: | 1. Faculty of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel;2. Israeli CFD Center, Caesarea Industrial Park 38900, Israel;3. Computer Science Department, Technion, Israel Institute of Technology, Haifa 32000, Israel |
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Abstract: | 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. |
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Keywords: | RANS Turbulence model Positivity preservation Numerical stiffness Source term Multigrid |
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