Data-parallel lower-upper relaxation method for the Navier-Stokes equations

Abstract

The lower-upper symmetric Gauss-Seidel method is modified for the simulation of viscous flows on massively parallel computers. The resulting diagonal data-parallel lower-upper relaxation (DP-LUR) method is shown to have good convergence properties on many problems. However, the convergence rate decreases on the high cell aspect ratio grids required to simulate high Reynolds number flows. Therefore, the diagonal approximation is relaxed, and a full matrix version of the DP-LUR method is derived. The full matrix method retains the data-parallel properties of the original and reduces the sensitivity of the convergence rate to the aspect ratio of the computational grid. Both methods are implemented on the Thinking Machines CM-5, and a large fraction of the peak theoretical performance of the machine is obtained. The low memory use and high parallel efficiency of the methods make them attractive for large-scale simulation of viscous flows.