A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations

Abstract

We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.