A new multigrid approach to convection problems

Abstract

A new multigrid method for convection problems is presented. It is designed to overcome the problem of alignment, the flow being aligned with the grid. The technique employs semi-coarsening in several directions simultaneously and gives rise to multiple coarser grids with the same total number of points per grid-level, but with different sizes in each co-ordinate direction. The amount of work per multigrid cycle is still O(N). As an example, the method is applied to the nonlinear upwind-differenced Euler equations of gas dynamics in two dimensions. Convergence rates are estimated by two-level Fourier analysis for the linearised equations. Numerical experiments on the nonlinear equations confirm these estimates.