关键词: 非等距网格离散 紧致差分格式 高精度 多重网格方法 部分半粗化

Abstract:

The two-dimensional （2D） convection-diffusion equation is solved by combining the superiority of the unequal mesh-size high-order compact differencescheme with the fast convergence of the multigrid method. It is shown that for solving the physical problems in which physical quantities show different characteristic states in different directions or different changing features, the proposed multigrid algorithm based on the fourth-order compact schem e and the standard central difference scheme with unequal mesh size is more efficient than that with an equal mesh size. In addition, the partial semicoarsening strategy is more efficient than full-coarsening with unequal mesh size discreitization. Among the multigrid algorithms of the fourth-order compact schemes, the most effective smoother is the line smoother. The muhigrid algorithm of the fourth-order compact scheme under unequal mesh size discretization is convergent for the large cell Reynold number in the 2D convection-diffusion problem.

Key words: unequal mesh-size diseretization, compact difference scheme, higher accuracy, multigrid method, partial semicoarsening