Highly accurate numerical methods for incompressible 3d fluid flows on parallel architectures

Abstract

We consider an approach to efficient parallel implementation of the high order Control Volume Padé-type Differences (CVPD) applied to spatial time-dependent flow in the mixing tanks. This numerical technology allows to obtain very high quality solutions on the block-structured curvilinear grids with sliding grid capability. In some sense it combines the flexibility of the finite volume methods with the accuracy of the spectral methods. However, the payoff for the high accuracy is that the parallel implementation issues become more complicated as compared to conventional low order approximation methods. Our objective is to demonstrate that reasonable parallel efficiency can be attainedo n the parallel computer platforms without compromising the high accuracy, when the highly accurate non-local discrete operators and implicit time-steppings are usedas the building blocks of the numerical methods. We present numerical results obtained on CRAY C90, CRAY T3D andI BM SP2.