A high performance algorithm for incompressible flows using local solenoidal functions

The convergence of iterative methods used to solve the linear systems arising in incompressible flow problems is sensitive to flow parameters such as the Reynolds number; time step and the mesh width. This paper presents a class of algorithms to solve these linear systems using local solenoidal functions. An optimal preconditioner is described via an iterative method to solve the resulting reduced system. This paper also suggests inexpensive parallel matrix-vector products using bounded buffers for interprocessor communication. Experimental results for a three dimensional problem show that the preconditioning step need not be solved accurately at each iteration, thereby decreasing the time spent in the potentially expensive routine. These experiments also show that the proposed algorithm assures a constant rate of convergence across the range of flow parameter variation. Scalability of the algorithm is suggested by the experiments on the SGI Origin 2000.