Parallel Multigrid Solution of the Navier-Stokes Equations on General 2D-Domains

摘要

The paper describes a parallel multigrid solver for steady-state incompressible Navier-Stokes equations on general domains. Due to the geometrical generality of the problem, the approach is based on a non-staggered (nodal-point) finite volume scheme on multi-block boundary fitted grids. The typical instability of non-staggered schemes is overcome by suitably modifying the discrete continuity equation without affecting the overall order of consistency. Starting from the most simple Cartesian case, the authors discuss several possible multigrid approaches to the general 2D-problem. This motivates the basic design decision of the multigrid solver in regard to both the discretization and the choice of multigrid components (smoothing schemes). Furthermore, the principal technique of parallelization (grid partitioning) is described as well as some fundamental aspects of the implementation (communication library). (Copyright (c) GMD 1988.)