A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting

Type
Article

Authors
Guermond, Jean-Luc
Minev, Peter D.

KAUST Grant Number
KUS-C1-016-04

Date
2010-05

Abstract
A new direction-splitting-based fractional time stepping is introduced for solving the incompressible Navier-Stokes equations. The main originality of the method is that the pressure correction is computed by solving a sequence of one-dimensional elliptic problems in each spatial direction. The method is very simple to program in parallel, very fast, and has exactly the same stability and convergence properties as the Poisson-based pressure-correction technique, either in standard or rotational form. © 2010 Académie des sciences.

Citation
Guermond J-L, Minev PD (2010) A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting. Comptes Rendus Mathematique 348: 581–585. Available: http://dx.doi.org/10.1016/j.crma.2010.03.009.

Acknowledgements
This material is based upon work supported by the National Science Foundation grants DMS-0713829. This publication is also partially based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The work of P. Minev is also supported by fellowships from the Institute of Applied Mathematics and Computational Science and the Institute of Scientific Computing at Texas A&M University and a Discovery grant of NSERC.

Publisher
Elsevier BV

Journal
Comptes Rendus Mathematique

DOI
10.1016/j.crma.2010.03.009

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