Advertisement

A new second order positivity preserving kinetic schemes for the compressible Euler equations

  • Jean-Luc Estivalezes
  • Philippe Villedieu
3. Numerical Methods and Algorithms a) Kinetic/Boltzmann Schemes
Part of the Lecture Notes in Physics book series (LNP, volume 453)

Abstract

We present a new second order kinetic flux-splitting schemes for the compressible Euler equations and we prove that this scheme is positivity preserving (i.e ρ and T remain ≥ 0). Our first order kinetic scheme is based on the Maxwellian equilibrium function and was initially proposed by Pullin. Our higher order extension can be seen as a variant of the so called corrected anti-diffusive flux approach. The necessity of a limitation on the antidiffusive correction appears naturally in order to satisfy the constraint of positivity.

Keywords

Euler Equation Blast Wave Order Scheme Compressible Euler Equation Approximate Riemann Solver 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Deshpande, S. (1986): “On the Maxwellian distribution, symmetric form and entropy conservation for the Euler equations”, NASA Langley report 2583 Google Scholar
  2. [2]
    Einfeld, B., Munz, C., Roe,P.,Sjögreen,B. (1991): “On Godunov type methods near low density ”,Journal of Computational Physics, Vol 92, pp. 273–295CrossRefGoogle Scholar
  3. [3]
    Estivalezes, J.L., Villedieu,P. (1994): “High order positivity preserving kinetic schemes for the compressible Euler equations”, SIAM Journal of Numerical Analysis, submittedGoogle Scholar
  4. [4]
    Perthame, B. (1992): “Second order Boltzmann schemes for gas compressible Euler equations in one and two space dimensions”, SIAM Journal of Numerical Analysis, Vol 27, pp. 1405–1421CrossRefGoogle Scholar
  5. [5]
    Prendergast, K. H., Xu, K. (1993): “Numerical hydrodynamics from gas kinetic theory”, Journal of Computational Physics, Vol 109, pp. 53–66CrossRefGoogle Scholar
  6. [6]
    Pullin, D. (1980): “Direct simulations methods for compressible inviscid ideal gas-flows”, Journal of Computational Physics, Vol 34, pp. 231–244CrossRefGoogle Scholar
  7. [7]
    Villedieu, P., Mazet, P. (1994): “Schémas cinétiques pour les équations d'Euler hors équilibre thermochimique”, La Recherche Aérospatiale, accepted for publicationGoogle Scholar
  8. [8]
    Woodward, P., Collela, P. (1984): “The numerical simulation of two-dimensional fluid flow with strong shocks”, Journal of Computational Physics, Vol 54, pp. 115–173CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jean-Luc Estivalezes
    • 1
  • Philippe Villedieu
    • 2
  1. 1.ONERA-CERTToulouse cedexFrance
  2. 2.MIP, Unité mixte CNRSUniversité de Toulouse IIIToulouse cedexFrance

Personalised recommendations