A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach

Kazufumi Ito; Zhonghua QIAO

doi:10.1016/j.jcp.2008.05.021

A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach

Kazufumi Ito, Zhonghua QIAO^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

34 Citations (Scopus)

Abstract

This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.

Original language	English
Pages (from-to)	8177-8190
Number of pages	14
Journal	Journal of Computational Physics
Volume	227
Issue number	17
DOIs	https://doi.org/10.1016/j.jcp.2008.05.021
Publication status	Published - 1 Sept 2008

Scopus Subject Areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Compact fourth order MAC finite difference scheme
Staggered grid
Stokes equations

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10.1016/j.jcp.2008.05.021

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title = "A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach",

abstract = "This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.",

keywords = "Compact fourth order MAC finite difference scheme, Staggered grid, Stokes equations",

author = "Kazufumi Ito and Zhonghua QIAO",

note = "Funding Information: The authors were partially supported by the Office of Naval Research under Grant M00014-06-1-0067 and the Air Force Office of Scientific Research under Grant FA9550-06-1-0241. ",

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AU - Ito, Kazufumi

AU - QIAO, Zhonghua

N1 - Funding Information: The authors were partially supported by the Office of Naval Research under Grant M00014-06-1-0067 and the Air Force Office of Scientific Research under Grant FA9550-06-1-0241.

PY - 2008/9/1

Y1 - 2008/9/1

N2 - This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.

AB - This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.

KW - Compact fourth order MAC finite difference scheme

KW - Staggered grid

KW - Stokes equations

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 17

ER -

A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach

Abstract

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