Section: New Results

Solving Navier-Stokes equations on heterogeneous parallel architectures

Participants : Marc Baboulin, Jack Dongarra, Joël Falcou, Yann Fraigneau, Olivier Lemaître, Yushan Wang.

The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. We implemented a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We applied the prediction-projection method which transforms the Navier-Stokes equations into three Helmholtz equations and one Poisson equation. For each Helmholtz system, we applied 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. Our implementation is 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 provided performance results on a current multicore system.[31]