Algebraic multigrid within defect correction for the linearized Euler equations

Abstract

Given the continued difficulty of developing geometric multigrid methods that provide robust convergence for unstructured discretizations of compressible flow problems in aerodynamics, we turn to algebraic multigrid (AMG) as an alternative with the potential to automatically deal with arbitrary sources of stiffness on unstructured grids. We show here that AMG methods are able to solve linear problems associated with first-order discretizations of the compressible Euler equations extremely rapidly. In order to solve the linear problems resulting from second-order discretizations that are of practical interest, we employ AMG applied to the first-order system within a defect correction iteration. It is demonstrated on two-and three-dimensional test cases in a range of flow regimes (sub-, trans-and supersonic) that the described method converges rapidly and robustly. © 2010 John Wiley & Sons, Ltd.