research-article

Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

Authors:

P. MoinAuthors Info & Claims

Journal of Computational Physics, Volume 143, Issue 1

Pages 90 - 124

https://doi.org/10.1006/jcph.1998.5962

Published: 10 June 1998 Publication History

Abstract

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass, momentum, and kinetic energy. This deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems. Finite difference schemes in a collocated grid system are also analyzed, and a violation of kinetic energy conservation is revealed. The predicted conservation properties are demonstrated numerically in simulations of inviscid white noise, performed in a two-dimensional periodic domain. The proposed fourth order schemes in a staggered grid system are generalized for the case of a non-uniform mesh, and the resulting scheme is used to perform large eddy simulations of turbulent channel flow.

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Index Terms

Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow
1. Applied computing
  1. Physical sciences and engineering
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 143, Issue 1

June 10, 1998

290 pages

ISSN:0021-9991

Editor:
J. U. Brackbill
Los Alamos National Lab, Los Alamos, NM

Issue’s Table of Contents

Copyright © Academic Press.

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 10 June 1998

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https://dl.acm.org/doi/10.1016/j.jcp.2024.112972
Edoh A(2024)Conservative correction procedures utilizing artificial dissipation operatorsJournal of Computational Physics10.1016/j.jcp.2024.112880504:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.112880
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