TY - JOUR

T1 - A parallel solver for incompressible fluid flows

AU - Wang, Yushan

AU - Baboulin, Marc

AU - Dongarra, Jack

AU - Falcou, Joël

AU - Fraigneau, Yann

AU - Le Maître, Olivier

N1 - Funding Information:
This work was supported by Région ˆle-de-France and Digitéo (http://www.digiteo.fr), CALIFHA project, contract No 2011-038D. We also thank Pierre Esterie (University Paris-Sud) for his support in using Boost SIMD.

PY - 2013

Y1 - 2013

N2 - The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. 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.

AB - The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. 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.

KW - ADI

KW - Navier-stokes equations

KW - Parallel computing

KW - Partial diagonalization

KW - Prediction-projection

KW - SIMD

UR - http://www.scopus.com/inward/record.url?scp=84893957675&partnerID=8YFLogxK

U2 - 10.1016/j.procs.2013.05.207

DO - 10.1016/j.procs.2013.05.207

M3 - Conference article

AN - SCOPUS:84893957675

VL - 18

SP - 439

EP - 448

JO - Procedia Computer Science

JF - Procedia Computer Science

SN - 1877-0509

T2 - 13th Annual International Conference on Computational Science, ICCS 2013

Y2 - 5 June 2013 through 7 June 2013

ER -