Fast and high accuracy multiscale multigrid method with multiple coarse grid updating strategy for the 3D convection–diffusion equation

An improved multiscale multigrid method with multiple coarse grid updating strategy for a three dimensional convection–diffusion equation is presented. The novelty of the proposed method lies in a fine grid updating strategy arising from the idea of multiple coarse grid computation. The new fine grid updating strategy is able to replace the iterative refinement procedure in the existing multiscale multigrid method (Wang and Zhang, 2010) [16] to obtain high order solutions. Since the proposed method needs a fourth order compact scheme with unequal-meshsize grids, a 19 point fourth order compact difference scheme with unequal meshsize in different coordinate directions is also developed for the three dimensional convection–diffusion equation. Numerical results are given to compare the computed accuracy and the computational efficiency of the multiscale multigrid method with the multiple coarse grid updating strategy against the multiscale multigrid method with the iterative refinement procedure.