A Parallel Solver for Incompressible Fluid Flows

TitleA Parallel Solver for Incompressible Fluid Flows
Publication TypeConference Paper
Year of Publication2013
AuthorsWang, Y., M. Baboulin, J. Falcou, Y. Fraigneau, and O. Le Maître
Conference NameInternational Conference on Computational Science (ICCS 2013)
Date Published2013-06
PublisherElsevier B.V.
Conference LocationBarcelona, Spain
KeywordsADI, Navier-Stokes equations, Parallel computing, Partial diagonalization, Prediction-projection, SIMD

The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlin- earity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply the prediction-projection method which transforms the Navier-Stokes equations into three Helmholtz equations and one Poisson equation. For each Helmholtz system, we apply the Alternating Direction Implicit (ADI) method resulting in three tridiagonal systems. The Poisson equation is solved using partial diagonalization which transforms the Laplacian operator into a tridiagonal one. We describe an implementation based on MPI where the computations are performed on each subdomain and information is exchanged on the interfaces, and where the tridiagonal system solutions are accelerated using vectorization techniques. We present performance results on a current multicore system.