Mean-Flow-Multigrid for Implicit Reynolds-Stress-Model Computations

The purpose of this work is to develop an efficient and robust multigrid acceleration technique for the computation of the compressible Favre Reynolds averaged Navier Stokes equations with seven equation Reynolds stress model turbulence closures. The basic monogrid algorithm uses an upwind biased (symbol omitted) (deltachi3) flux vector split space discretization with implicit time integration. The discrete system of nonlinear equations is solved by a subiterative procedure, based on a local dual time stepping technique, which includes quasi Newton iteration in the limit deltatau leads to infinity. Full approximation scheme sawtooth cycle multigrid is applied on the mean flow variables only, while turbulence variables are simply injected into coarser grids. Characteristic baged multigrid is used for the restriction operator. The straightforward extension of the method to lower level two equation kappa Epsilon closures is described. Computational examples for various two and three dimensional complex flows, including large separation and/or shock wave/boundary layer interactions using different turbulence models, demonstrate that speed ups of 3 to 4 are obtained, using three levels of multigrid (fine + two coarser grids). [PUBLICATION ABSTRACT]