Abstract: In this paper, We apply FVE method to discrete INS equations with the original variable, In which the bilinear square finite element and the square finite volume are choiced, The discrete schemes of INS equations are presented. The FMV Multigrid algorithem is applied to solve that discrete system, Where DGS iteration is used as smoother, DGS distributive mode for the INS discrete system is also presented. The sample problems for the square cavity flow with Reynolds number Re≤100 are successfully calculated. The numerical solutions show that the results with 1FMV is satisfactory and when Re is not large, The FVE discrete scheme of the conserative INS equations and that of non-conserative INS equations with linearization both can provide almost same accuracy.

Key words: finite volume element method, Navier-Stokes equations, multigrid method, distributive Gauss-Seidel ralaxation method