A domain decomposition method for almost incompressible flow (Q1369545)

A domain decomposition method for solving the Navier-Stokes equations for almost incompressible flow is examined. At the price of a nonuniform decomposition of the domain, we have fast solvers in all subdomains. Hence, each iteration on the Schur complement system can be performed very efficiently. We have shown theoretically that the method requires much fewer memory positions and arithmetic operations than a direct method. Numerical experiments show that the iteration on the Schur complement system converges very fast. We also show that the spatial grid ratio might be crucial for the performance of the method.