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Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids

Publication ,  Journal Article
E, W; Liu, JG
Published in: Journal of Computational Physics
November 15, 1997

Simple, efficient, and accurate finite difference methods are introduced for 3D unsteady viscous incompressible flows in the vorticity-vector potential formulation on nonstaggered grids. Two different types of methods are discussed. They differ in the implementation of the normal component of the vorticity boundary condition and consequently the enforcement of the divergence free condition for vorticity. Both second-order and fourth-order accurate schemes are developed. A detailed accuracy test is performed, revealing the structure of the error and the effect of how the convective terms are discretized near the boundary. The influence of the divergence free condition for vorticity to the overall accuracy is studied. Results on the cubic driven cavity flow at Reynolds number 500 and 3200 are shown and compared with that of the MAC scheme. © 1997 Academic Press.

Duke Scholars

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

November 15, 1997

Volume

138

Issue

1

Start / End Page

57 / 82

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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E, W., & Liu, J. G. (1997). Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids. Journal of Computational Physics, 138(1), 57–82. https://doi.org/10.1006/jcph.1997.5815
E, W., and J. G. Liu. “Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids.” Journal of Computational Physics 138, no. 1 (November 15, 1997): 57–82. https://doi.org/10.1006/jcph.1997.5815.
E, W., and J. G. Liu. “Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids.” Journal of Computational Physics, vol. 138, no. 1, Nov. 1997, pp. 57–82. Scopus, doi:10.1006/jcph.1997.5815.
Journal cover image

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

November 15, 1997

Volume

138

Issue

1

Start / End Page

57 / 82

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences