DATA-PARALLEL LOWER-UPPER RELAXATION METHOD FOR THE NAVIER-STOKES EQUATIONS

The lower-upper symmetric Gauss-Seidel method is modified for the simu lation of viscous flows on massively parallel computers. The resulting diagonal data-parallel lower-upper relaxation (DP-LUR) method is show n to have good convergence properties on many problems. However, the c onvergence rate decreases on the high cell aspect ratio grids required to simulate high Reynolds number hows. Therefore, the diagonal approx imation is relaxed, and a full matrix version of the DP-LUR method is derived. The full matrix method retains the data-parallel properties o f the original and reduces the sensitivity of the convergence rate to the aspect ratio of the computational grid. Both methods are implement ed on the Thinking Machines CM-5, and a large fraction of the peak the oretical performance of the machine is obtained, The low memory use an d high parallel efficiency of the methods make them attractive for lar ge-scale simulation of viscous flows.