Skip to main content
Journal cover image

Essentially compact schemes for unsteady viscous incompressible flows

Publication ,  Journal Article
Weinan, E; Liu, JG
Published in: Journal of Computational Physics
January 1, 1996

A new fourth-order accurate finite difference scheme for the computation of unsteady viscous incompressible flows is introduced. The scheme is based on the vorticity-stream function formulation. It is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions. It is also very efficient, at every time step or Runge-Kutta stage, only two Poisson-like equations have to be solved. The Poisson-like equations are amenable to standard fast Poisson solvers usually designed for second order schemes. Detailed comparison with the second-order scheme shows the clear superiority of this new fourth-order scheme in resolving both the boundary layers and the gross features of the flow. This efficient fourth-order scheme also made it possible to compute the driven cavity flow at Reynolds number 106 on a 10242 grid at a reasonable cost. Fourth-order convergence is proved under mild regularity requirements. This is the first such result to our knowledge. © 1996 Academic Press, Inc.

Duke Scholars

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

January 1, 1996

Volume

126

Issue

1

Start / End Page

122 / 138

Related Subject Headings

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

Citation

APA
Chicago
ICMJE
MLA
NLM
Weinan, E., & Liu, J. G. (1996). Essentially compact schemes for unsteady viscous incompressible flows. Journal of Computational Physics, 126(1), 122–138. https://doi.org/10.1006/jcph.1996.0125
Weinan, E., and J. G. Liu. “Essentially compact schemes for unsteady viscous incompressible flows.” Journal of Computational Physics 126, no. 1 (January 1, 1996): 122–38. https://doi.org/10.1006/jcph.1996.0125.
Weinan E, Liu JG. Essentially compact schemes for unsteady viscous incompressible flows. Journal of Computational Physics. 1996 Jan 1;126(1):122–38.
Weinan, E., and J. G. Liu. “Essentially compact schemes for unsteady viscous incompressible flows.” Journal of Computational Physics, vol. 126, no. 1, Jan. 1996, pp. 122–38. Scopus, doi:10.1006/jcph.1996.0125.
Weinan E, Liu JG. Essentially compact schemes for unsteady viscous incompressible flows. Journal of Computational Physics. 1996 Jan 1;126(1):122–138.
Journal cover image

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

January 1, 1996

Volume

126

Issue

1

Start / End Page

122 / 138

Related Subject Headings

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