Domain decomposition implementations for parallel solutions of 3-D Navier- Stokes equations

Abstract

The Domain Decomposition Method (DDM) is an efficient way of handling large-scale flow problems. Since its introduction to the CFD community, various types and numerous implementations have appeared in the literature. The most efficient type is the non-overlapping DDM, which enables one to handle the interface conditions smoothly. Hence, using non-overlapping DDM, super-linear speed-up is possible even for solutions obtained on clusters of workstations. In this chapter, two different domain decomposition methods are implemented for the parallel solution of the Poisson's equation arising in the numerical analysis of the incompressible flow problems. The Poisson's equation is written both in terms of pressure and auxiliary potential. As a test case, the cubic cavity problem is analyzed with both methods and formulations. In light of cavity results, flow about a complex geometry, wing-winglet configuration, is analyzed using the more efficient domain decomposition method. Pressure and auxiliary potential formulation solutions are compared in terms of accuracy, computation time and parallel efficiency.