A Local Mesh Refinement Multigrid Method for 3-D Convection Problems with Strongly Variable Viscosity

A numerical method for solving 3-D convection problems with variable viscosity in Cartesian geometry is presented. Equations for conservation of mass, momentum, and energy are solved using a second-order finite-volume discretization in combination with a multigrid method. Viscosity variations of 10 orders of magnitude are considered. Convergence deteriorates with increasing viscosity variations, but modifications of the multigrid algorithm are found to improve the robustness of the numerical method for very large viscosity contrasts. An efficient and flexible local mesh refinement technique is presented which is applied to various convection problems with variable viscosity. Comparisons with other numerical methods reveal that accurate results are obtained even when viscosity varies strongly.