Solution of viscous fluid flows on a distributed memory concurrent computer

Abstract

AbstractA concurrent algorithm for the solution óf the Navier–Stokes equations expressed in curvilinear co‐ordinates has been developed for execution on a distributed memory parallel computer. This algorithm offers the ultimate promise of near‐supercomputer performance on relatively low‐cost parallel computers. The new algorithm is based on an existing serial pressure‐correction‐based algorithm, and uses domain decomposition to partition the problem onto the processors. The algorithm is demonstrated on an Intel iPSC for a complicated two‐dimensional laminar flow problem, for various grid sizes and numbers of processors. Initial results based on straightforward domain decomposition showed that the speed‐up per iteration approached 100% parallel efficiency as the grid size was increased, but that the convergence rate of the algorithm deteriorated relative to the original serial algorithm as the number of processors was increased, limiting the speed‐up achieved. This degradation in convergence rate was traced to a poorer solution of the pressure correction equation in the concurrent procedure. The addition of a global block correction procedure, implemented via efficient global communications routines, remedied this problem, making the convergence rate of the concurrent procedure equivalent to the serial algorithm. The maximum speed‐up achieved with the revised concurrent algorithm was a factor of 12·3 with 16 processors, representing a parallel efficiency of 77%.