Numerical solutions of Euler equations by using a new flux vector splitting scheme

GeCheng Zha, E. Bilgen

Research output: Contribution to journalArticle

73 Citations (Scopus)

Abstract

A new flux vector splitting scheme has been suggested in this paper. This scheme uses the velocity component normal to the volume interface as the characteristic speed and yields the vanishing individual mass flux at the stagnation. The numerical dissipation for the mass and momentum equations also vanishes with the Mach number approaching zero. One of the diffusive terms of the energy equation does not vanish. But the low numerical diffusion for viscous flows may be ensured by using higher-order differencing. The scheme is very simple and easy to be implemented. The scheme has been applied to solve the one dimensional (1D) and multidimensional Euler equations. The solutions are monotone and the normal shock wave profiles are crisp. For a 1D shock tube problem with the shock and the contact discontinuities, the present scheme and Roe scheme give very similar results, which are the best compared with those from Van Leer scheme and Liou-Steffen's advection upstream splitting method (AUSM) scheme. For the multidimensional transonic flows, the sharp monotone normal shock wave profiles with mostly one transition zone are obtained. The results are compared with those from Van Leer scheme, AUSM and also with the experiment.

Original languageEnglish
Pages (from-to)115-144
Number of pages30
JournalInternational Journal for Numerical Methods in Fluids
Volume17
Issue number2
StatePublished - Jul 1 1993
Externally publishedYes

Fingerprint

flux vector splitting
Euler equations
shock wave profiles
Advection
normal shock waves
Euler Equations
Shock waves
Numerical Solution
Fluxes
advection
upstream
Transonic flow
Shock tubes
Viscous flow
Mach number
Momentum
Mass transfer
transonic flow
shock tubes
viscous flow

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics
  • Condensed Matter Physics

Cite this

Numerical solutions of Euler equations by using a new flux vector splitting scheme. / Zha, GeCheng; Bilgen, E.

In: International Journal for Numerical Methods in Fluids, Vol. 17, No. 2, 01.07.1993, p. 115-144.

Research output: Contribution to journalArticle

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