Improving the resolution of an elliptic solver for CFD problems on the grid

The chapter focuses on the fast resolution of elliptic problems generated by algorithms to solve computational fluid dynamics (CFD) problems. A typical application is a pressure solver in an incompressible Navier-Stokes flow code. The chapter describes a domain decomposition method that is numerically efficient, scales well on a parallel computer, and is highly tolerant to the high latency and low bandwidth of a slow network. The method is based on the implementation of a domain decomposition technique in parallel and also on the performance tuning of the linear solver depending on the sub domain and the processor architecture. The chapter presents a domain decomposition for elliptic solver that is interesting for distributed computing with high latency network that provides good scalability results. The chapter demonstrates impact of the choice of the sub domain solver and presents a methodology with surface response that can help to tune the solver in an optimal way. While generating such a model is cumbersome and time consuming, there are advantages of generating them in an automatic manner using the resources of the grid.