Convergence Acceleration on Unstructured Meshes

Abstract

An implicit residual smoothing technique to enhance convergence properties of Runge-Kutta time stepping schemes on unstructured meshes is developed. In contrast to standard implicit residual smoothing schemes applied on structured meshes, no direct information about the cell aspect ratio is required. The development of the acceleration technique is based on the Mach number based Advection Pressure Splitting (MAPS) spatial discretization. With the new implicit smoothing, maximum CFL numbers comparable to those on structured meshes are obtainable for unstructured meshes, and in combination with multigrid acceleration, convergence rates similar to structured codes are achieved. In order to allow the solution of incompressible flows, the implicit residual smoothing is adapted to low Mach number preconditioning.