An Upwind Multigrid Method for Solving Viscous Flows on Unstructured Triangular Meshes

A multigrid algorithm is combined with an upwind scheme for solving the twodimensional Reynolds-averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe’s flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multielement airfoils, including inviscid, laminar and turbulent flows. The results show an appreciable speedup of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.