Multigrid solution of convection problems with strongly variable viscosity

Abstract

Summary We investigate the robustness and efficiency of various multigrid (MG) algorithms used for simulation of thermal convection with strongly variable viscosity. We solve the hydrodynamic equations in the Boussinesq approximation, with infinite Prandtl number and temperature- and depth-dependent viscosity in two dimensions. A full approximation storage (FAS) MG method with a symmetric coupled Gauss–Seidel (SCGS) smoother on a staggered grid is used to solve the continuity and Stokes equations. Time stepping of the temperature equation is done by an alternating direction implicit (ADI) method. A systematic investigation of different variants of the algorithm shows that modifications in the MG cycle type, the viscosity restriction, the smoother and the number of smoothing operations are significant. A comparison with a well-established finite element code, utilizing direct solvers, demonstrates the potentials of our method for solving very large equation systems. We further investigate the influence of the lateral boundary conditions on the geometrical structure of convective flow. Although a strong influence exists, even in the case of very wide boxes, a systematic difference between periodic and symmetric boundary conditions, regarding the preferred width of convection cells, has not been found.