Convergence Analysis of Pressure-Velocity Iteration Methods for Solving Unsteady Navier-Stokes Equations

摘要

Due to the implementation of numerical solution algorithms for the nonstationary Navier-Stokes equations of anincompressible fluid on massively parallel computers iterative methods are of special interest. A red-black pressure-velocity-iteration which allows an efficient parallelization based on a domain decomposition [1] willbe analyzed in this paper. We prove the equivalence of the pressure-velocity-iteration (PUI) by Chorin/Hirt/Cook [2][3] with a SOR-iteration tosolve a poisson equation for the pressure. We show this on a 2D rectangle with some special outflow boundary conditions andDirichlet data for the velocity elsewhere. This equivalence allows us to prove the convergence of that iteration scheme.