Incompressible Navier-Stokes solver using extrapolation method suitable for massively parallel computing

The authors propose combination of the coupled method and the extrapolation method as a numerical technique suitable for calculation of an incompressi ble flow on a massively parallel computer. In the coupled method, the momen tum equations and the continuity equation are directly coupled, and velocit y components and pressure values are simultaneously updated. It is very sim ple and efficiently parallelized. The extrapolation method is an accelerati ve technique predicting a converged solution from a sequence of intermediat e solutions generated by an iterative procedure. When it is implemented on a parallel computer, it is expected to retain good accelerative property ev en for fine granularity in contrast to the multigrid method. In this paper three existing versions of the extrapolation method, ROLE, MPE and ROGE, ar e reviewed, and LWE, a new version developed by the authors, is presented. Then, ROLE and LWE are applied to numerical analysis of Poisson's equation on a Fujitsu AP1000 and its results are shown. The mathematical proof that the extrapolation method, which is based on the linear theory, is applicabl e to an iterative procedure solving nonlinear equations is presented. Then the code consisting of the coupled method and the extrapolation method is i mplemented on a Fujitsu AP1000 to solve two simple 2-D steady flows. Accele rative property of the extrapolation method is discussed, and suitability o f the code to massively parallel computing is demonstrated.