Robustness of coupled Algebraic Multigrid for the Navier-Stokes equations

Abstract

A new implementation of the Algebraic Multigrid method is presented. It is applied to the coupled linearized discrete equations arising from an implicit pressure-based finite volume discretization of the 3D Navier-Stokes equations on structured or unstructured meshes. It employs a grid-coarsening algorithm based on an evaluation of relative coefficient strengths. The restriction and prolongation operators are those implied by the Additive Correction Multigrid method. The relaxation scheme is a coupled Incomplete Lower Upper factorization, and the W-Cycle is used. The results of the coarsening algorithm applied to two 2D model problems is visualized and discussed. Verification of performance is made on several very different CFD applications relevant to the aerospace field. These include incompressible to supersonic, external and internal, stationary and rotating, reacting and nonreacting flows. In all cases the exact same multigrid method is used. Thus the feasibility of using Algebraic Multigrid as the linear equation solver for an implicit CFD method that must handle diverse applications is shown. The limitations and weaknesses of the method are also described. (Author)