| Abstract: | This paper describes a domain decomposition numerical procedure for solving the Navier-Stokes equations in regions with complex geometries. The numerical method includes a modified version of QUICK (quadratic upstream interpolation convective kinematics) for the formulation of convective terms and a central difference scheme for the diffusion terms. A second-order-accurate predictor-corrector scheme is employed for the explicit time stepping. Although the momentum equations are solved independently on each subdomain, the pressure field is computed simultaneously on the entire flow field. A multigrid technique coupled with a Schwarz-like iteration method is devised to solve the pressure equation over the composite domains. The success of this strategy depends crucially on appropriate methods for specifying intergrid pressure boundary conditions on subdomains. A proper method for exchanging information among subdomains during the Schwarz sweep is equally important to the success of the multigrid solution for the overall pressure field. These methods are described and subsequently applied to two forced convection flow problems involving complex geometries to demonstrate the power and versatility of the technique. The resulting pressure and velocity fields exhibit excellent global consistency. The ability to simulate complex flow fields with this method provides a powerful tool for analysis and prediction of mixing and transport phenomenon. |
