Abstract: An efficient method for multiple-scale problems is presented, which extends the authors' modified Temam scheme on the staggered mesh [5] to nonuniform staggered mesh. The nonuniform mesh is generated by a continuous coordinate transformation without singlarity according to boundary layer thickness so as to ensure accuracy. The constraint condition, i.e. continuity equation, is realized by the pressure correction projection method; the related Poisson equation on nonuniform mesh is solved by the generalized cyclic reduction program from FISHPACK. Numerical simulation of driven flow in a square cavity was done for steady-state solutions for Re=100, 400, 1000, 5000. These solutions accurately match those given in literature; for high Reynold numbers, tertiary vortices near the corners in the cavity are resolved. These results shows that with suitable nonuniform mesh, the above method remarkably improves computational efficiency.

Key words: modified Temam scheme, nonuniform staggered mesh, driven square cavity flow