Incompressible Navier-Stokes Solver with Extrapolation Method Suitable for Massively Parallel Computing : Application of Extrapolation Method to Linear Equation

Abstract

A massively parallel computer, which has a large number of processors, is expected to become the main instrument for scientific numerical analysis including the CFD field. It has been pointed out that efficiency of parallel computing becomes worse when the number of processors increases and granularity comes to fine. Therefore an accelerative technique should be introduced to achieve nearly maximum performance of the massively parallel computer. Some researchers have used the multigrid method, but this technique turned out to be inappropriate for parallel computing of very fine granularity because efficiency rapidly worsens. The purpose of this study is to propose a numerical technique suitable for calculation of incompressible flow on massively parallel computer. In this regard, we choose an extrapolation method as the accelerative technique, which perdicts converged solutions from a suquence of intermediate solutions and is expected to retain its accelerative property for fine granularity. Three existing extrapolation methods ROLE, MPE, ROGE and newly developed LWE are discussed. Furthermore, ROLE and LWE are applied to numerical analysis of Poisson's equation and the results are discussed.