Multigrid solution of convection problems with strongly variable viscosity

We investigate the robustness and efficiency of various multigrid (Nlc) alg orithms used for simulation of thermal convection with strongly variable vi scosity. We solve the hydrodynamic equations in the Boussinesq approximatio n, with infinite Prandtl number and temperature- and depth-dependent viscos ity 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 temperat ure equation is done by an alternating direction implicit (ADI) method. A s ystematic investigation of different variants of the algorithm shows that m odifications 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, demonstrat es the potentials of our method for solving very large equation systems. We further investigate the influence of the lateral boundary conditions on th e geometrical structure of convective flow. Although a strong influence exi sts, even in the case of very wide boxes, a systematic difference between p eriodic and symmetric boundary conditions, regarding the preferred width of convection cells, has not been found.