An efficient upwind/relaxation algorithm for the Euler and Navier–Stokes equations

Ge‐Cheng ‐C Zha, Dao‐Zhi ‐Z Liu, Tie‐You ‐Y Ma

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


An efficient Euler and full Navier-Stokes solver based on a flux splitting scheme is presented. The original Van Leer flux vector splitting form is extended to arbitrary body-fitted co-ordinates in the physical domain so that it can be used with a finite volume scheme. The block matrix is inverted by Gauss-Seidel iteration. It is verified that the often used reflection boundary condition will produce incorrect flux crossing the wall and cause too large numerical dissipation if flux vecor splitting is used. To remove such errors, an appropriate treatment of wall boundary conditions is suggested. Inviscid and viscous steady transonic internal flows are analyzed, including the case of shock-induced boundary layer separation.

Original languageEnglish (US)
Pages (from-to)517-529
Number of pages13
JournalInternational Journal for Numerical Methods in Fluids
Issue number5
StatePublished - May 1989
Externally publishedYes


  • Flux splitting
  • Implicit scheme
  • Transonic flow

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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