Additive multigrid with scaled correction for implicit compressible flow solvers

Application of additive multigrid with scaled correction for implicit solvers of the compressible Reynolds-averaged Navier-Stokes (RANS) equations is presented. Using multiplicative V-cycle multigrid to solve RANS equations in parallel typically results in poor parallel efficiency on the coarser grids. To alleviate these issues, additive multigrid can be used, since it exhibits better parallel efficiency. However, additive multigrid is typically observed to be slower than multiplicative multigrid and, in some cases it may not even converge. In this work, the convergence rate of additive multigrid is improved significantly through scaling the correction. Convergence of the approach compared to V-cycle is demonstrated for RANS equations on several external aerodynamics cases. In light of emerging massively parallel hardware for scientific computing, the applicability of the asynchronous fine-grain parallel smoothers to the proposed method is verified.