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

Abstract

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 O(Δx 3 ) 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 Δt → ∞. Full-approximation scheme sawtooth cycle multigrid is applied on the mean-flow variables only, while turbulence variables are simply injected into coarser grids. Characteristic-based multigrid is used for the restriction operator. The straightforward extension of the method to lower-level two-equation k-e 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).