Comparison between pressure gradient method and MAC method on high Re calculation

A cavity flow driven by shear and buoyancy forces is used as a test problem in the application of a nonstaggered pressure gradient (PG) method in solving the two-dimensional incompressible Navier-Stokes equations. Twelve finite differencing schemes are used to solve the cavity flow problem. The schemes consist of various combinations of grid arrangements, upwinding treatments, and conservativeness of convection terms. An artificial source term is introduced, and the solutions are compared with those obtained by the conventional marker-and-cell (MAC) method. The comparisons favor the PG method. Numerical results obtained by the twelve schemes are compared with exact solutions in order to assess the stability and accuracy of each scheme.