The robustness issue on multigrid schemes applied to the Navier-Stokes equations for laminar and turbulent, incompressible and compressible flows

摘要

The paper's leitmotiv is condensed in one word: robustness. This is a real hindrance for the successful implementation of any multigrid scheme for solving the Navier-Stokes set of equations. In this paper, many hints are given to improve this issue. Instead of looking for the best possible speed-up rate for a particular set of problems, at a given regime and in a given condition, the authors propose some ideas pursuing reasonable speed-up rates in any situation. In a previous paper, the authors presented a multigrid method for solving the incompressible turbulent RANS equations, with particular care in the robustness and flexibility of the solution scheme. Here, these concepts are further developed and extended to compressible laminar and turbulent flows. This goal is achieved by introducing a non-linear multigrid scheme for compressible laminar (NS equations) and turbulent flow (RANS equations), taking benefit of a convenient master-slave implementation strategy.