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Analysis of a fourth order finite difference method for the incompressible Boussinesq equations

Publication ,  Journal Article
Wang, C; Liu, JG; Johnston, H
Published in: Numerische Mathematik
May 1, 2004

The convergence of a fourth order finite difference method for the 2-D unsteady, viscous incompressible Boussinesq equations, based on the vorticity-stream function formulation, is established in this article. A compact fourth order scheme is used to discretize the momentum equation, and long-stencil fourth order operators are applied to discretize the temperature transport equation. A local vorticity boundary condition is used to enforce the no-slip boundary condition for the velocity. One-sided extrapolation is used near the boundary, dependent on the type of boundary condition for the temperature, to prescribe the temperature at "ghost" points lying outside of the computational domain. Theoretical results of the stability and accuracy of the method are also provided. In numerical experiments the method has been shown to be capable of producing highly resolved solutions at a reasonable computational cost.

Duke Scholars

Published In

Numerische Mathematik

DOI

ISSN

0029-599X

Publication Date

May 1, 2004

Volume

97

Issue

3

Start / End Page

555 / 594

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Wang, C., Liu, J. G., & Johnston, H. (2004). Analysis of a fourth order finite difference method for the incompressible Boussinesq equations. Numerische Mathematik, 97(3), 555–594. https://doi.org/10.1007/s00211-003-0508-3
Wang, C., J. G. Liu, and H. Johnston. “Analysis of a fourth order finite difference method for the incompressible Boussinesq equations.” Numerische Mathematik 97, no. 3 (May 1, 2004): 555–94. https://doi.org/10.1007/s00211-003-0508-3.
Wang C, Liu JG, Johnston H. Analysis of a fourth order finite difference method for the incompressible Boussinesq equations. Numerische Mathematik. 2004 May 1;97(3):555–94.
Wang, C., et al. “Analysis of a fourth order finite difference method for the incompressible Boussinesq equations.” Numerische Mathematik, vol. 97, no. 3, May 2004, pp. 555–94. Scopus, doi:10.1007/s00211-003-0508-3.
Wang C, Liu JG, Johnston H. Analysis of a fourth order finite difference method for the incompressible Boussinesq equations. Numerische Mathematik. 2004 May 1;97(3):555–594.
Journal cover image

Published In

Numerische Mathematik

DOI

ISSN

0029-599X

Publication Date

May 1, 2004

Volume

97

Issue

3

Start / End Page

555 / 594

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics