Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

Guermond, J.-L.; Salgado, Abner J.

Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

Type

Article

Authors

Guermond, J.-L.
Salgado, Abner J.

KAUST Grant Number

KUS-C1-016-04

Date

2011-01

Abstract

In this paper we analyze the convergence properties of a new fractional time-stepping technique for the solution of the variable density incompressible Navier-Stokes equations. The main feature of this method is that, contrary to other existing algorithms, the pressure is determined by just solving one Poisson equation per time step. First-order error estimates are proved, and stability of a formally second-order variant of the method is established. © 2011 Society for Industrial and Applied Mathematics.

Citation

Guermond J-L, Salgado AJ (2011) Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density. SIAM J Numer Anal 49: 917–944. Available: http://dx.doi.org/10.1137/090768758.

Acknowledgements

Received by the editors August 21, 2009; accepted for publication (in revised form) February 28, 2011; published electronically May 10, 2011. This publication is based on work supported by King Abdullah University of Science and Technology (KAUST) award KUS-C1-016-04.Department of Mathematics, Texas A&M University, College Station, TX 77843-3368 (guermond@math.tamu.edu). This author's work was partially supported by National Science Foundation grant NSF-DMS (0713829).