A fast, high resolution, second-order central scheme for incompressible flows

Raz Kupferman*, Eitan Tadmor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second- order extension of the classic Lax-Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. and Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. and Tadmor E. (1996) UCLA CAM Report 96- 36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Original languageAmerican English
Pages (from-to)4848-4852
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number10
StatePublished - 13 May 1997
Externally publishedYes


  • central difference schemes
  • hyperbolic conservation laws
  • nonoscillatory schemes
  • second-order accuracy


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