## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 439-448 |

Number of pages | 10 |

Journal | Procedia Computer Science |

Volume | 18 |

DOIs | |

State | Published - 2013 |

Event | 13th Annual International Conference on Computational Science, ICCS 2013 - Barcelona, Spain Duration: Jun 5 2013 → Jun 7 2013 |

### Bibliographical note

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.

## Keywords

- ADI
- Navier-stokes equations
- Parallel computing
- Partial diagonalization
- Prediction-projection
- SIMD

## ASJC Scopus subject areas

- General Computer Science