Development of a pressure-correction/ staggered-grid based multigrid solver for incompressible recirculating flows

A full multigrid/full approximation storage (FMG/FAS) algorithm is utilized to solve the incompressible recirculating flow problems in complex geometrics. The algorithm is implemented in conjunction with a pressure-correction/staggered-grid type of technique using curvilinear coordinates. In order to illustrate the performance of the method, two flow configurations—one a square cavity driven by a sliding top wall and the other a channel with multiple bumps—are used as test problems. Comparisons are made between the performances of the multigrid (MG) and single-grid methods, measured by the number of fine grid iterations, equivalent work units and CPU time. Besides demonstrating that the MG method can yield substantial speed-up with wide variations in Re, grid distributions and geometry, issues such as the convergence characteristics at different grid levels, the choice of convection schemes and the effectiveness of the basic iterative smoothers are studied. An adaptive grid scheme is also combined with the MG procedure to explore the effects of grid resolution on the MG convergence rate as well as the numerical accuracy.