A Special Multigrid Strategy on Non-Uniform Grids for Solving 3D Convection–Diffusion Problems with Boundary/Interior Layers

Boundary or interior layer problems of high-dimensional convection–diffusion equations have distinct asymmetry. Consequently, computational grid distributions and linear algebraic systems arising from finite difference schemes for them are also asymmetric. Numerical solutions these kinds more complicated than those symmetric problems. In this paper, we extended our previous work on the partial semi-coarsening multigrid method combined with high-order compact (HOC) scheme solving two-dimensional (2D) non-uniform grids to three-dimensional (3D) cases. The main merit present is that can be performed a different number in coordinate axes, which efficient same axes. experiments carried out validate accuracy efficiency method. It shown that, without losing high precision, very effective reduce computing cost by cutting down direction(s) does/do not contain boundary layer(s).