Aitken-Schwarz method for CFD solvers

This chapter describes the Aitken-Schwarz method for CFD (Computational Fluid Dynamic) solvers. The Schwarz algorithm has two important qualities that make its use in CFD applications very attractive. Firstly this method is very easy to implement on an existing CFD code and does not require a complete re-writing of the code. Secondly, the iteration step in a parallel implementation of the Schwarz algorithm is (memory) scalable thanks to the fact that communications are always among neighbor's sub-domains. Slow numerical convergence of the Schwarz algorithm is the main reason for which the Schwarz implementation is generally just a first step in parallelizing existing code. It is a classical approach to speed up the Schwarz method by combining the multilevel method with domain decomposition. However this technique generally implies a deep change in the data structure, in particular with unstructured grids that have large aspect ratio for meshes. This chapter is restricted to the two overlapping subdomain case and focuses on what might be done to make the method effective with general discretization, in particular for unstructured meshes or non matching grids.