Adaptive parallel multigrid in computational fluid dynamics

Abstract

In this paper the numerical and parallel efficiency of the adaptive parallel strategy employed in a multigrid-solver package LiSS, developed in GMD-SCAI, are discussed. Two main aspects in these issues are adaptive criterion and data-redistribution concept for load balancing. The adaptive criterion is based on the finite-element-residuals of governing equations. It can find refinement regions automatically, e.g. near shocks and geometric singularities. For parallelization new data in the adaptive phase can be re-distributed by sub-dividing and remapping the sub-blocks onto exisiting processors to obtain approximate load balancing. The 2D exmaples of Euler equations and incompressible Navier- Stokes equations in this paper show obviously high numerical and parallel efficiency of LiSS.