Fractional step artificial compressibility schemes for the unsteady incompressible Navier-Stokes equations

H. S. Tang, Fotis Sotiropoulos

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We propose a novel, time-accurate approach for solving the unsteady, three-dimensional, incompressible Navier-Stokes equations on non-staggered grids. The approach modifies the standard, dual-time stepping artificial-compressibility (AC) iteration scheme by incorporating ideas from pressure-based, fractional-step (FS) formulations. The resulting hybrid fractional-step/artificial-compressibility (FSAC) method is second-order accurate and advances the Navier-Stokes equations in time via a two-step procedure. In the first step, which is identical to the convection-diffusion step in pressure-based FS methods, a preliminary velocity field is calculated, which is not divergence-free. In the second step, however, instead of deriving a pressure-Poisson equation as in FS methods, the projection of the velocity field into the solenoidal vector space is implemented using a dual-time stepping AC formulation. Unlike the standard dual-time stepping AC formulations, where the dual-time iterations are carried out with the entire non-linear system, in the FSAC scheme the convective and viscous terms are computed only once or twice per physical time step. Numerical experiments show that the proposed method provides second-order accurate solutions and requires considerably less CPU time than the widely used standard AC formulation. To demonstrate its ability to compute complicate problems, the method is also applied to a flow past cylinder with endplates.

Original languageEnglish (US)
Pages (from-to)974-986
Number of pages13
JournalComputers and Fluids
Volume36
Issue number5
DOIs
StatePublished - Jun 2007

Bibliographical note

Funding Information:
The authors are grateful to the anonymous reviewers for their valuable suggestions. Dr. S.C. Jones also provided help on this work. This paper is sponsored by NSF CAREER award 9875691.

Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

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