Domain Decomposition Method for the Advection-Diffusion Equation

摘要

The report describes a model study for domain decomposition for theincompressible Navier-Stokes equations using the two-dimensional advection-diffusion equation. Three types of domain decomposition methods are investigated. They are: The Schwarz method; Neumann-Dirichlet coupling; and the Robbins-Robbins coupling. These three methods are discussed and compared with respect to robustness and efficiency. It turns out that the Neumann-Dirichlet algorithm is the most efficient, followed by Ribbons-Robbins and the Schwarz method. However, for flow nearly parallel to the block interfaces, convergence of the Neumann-Dirichlet method deteriorates and the Schwarz method is to be preferred. The Robbins-Robbins method combines the favorable convergence rates of the Neumann-Dirichlet method for flow normal to the interfaces with that of the Schwarz method for flow nearly parallel to the interfaces. Therefore, the Robbins-Robbins method is the most robust, followed by the Neumann-Dirichlet algorithm and the Schwarz method.