CALCOLO

, Volume 40, Issue 3, pp 163–194 | Cite as

On the use of symmetrizing variables for vacuums

  • T. Gallouët
  • J.-M. Hérard
  • N. Seguin
Article

Abstract

The paper is devoted to the computation of shallow-water equations (or Euler equations) in using an approximate Godunov scheme called VFRoe, when the flow may include dry areas (or very low density regions). This is achieved with the help of symmetrizing variables. Overall we are able to insure the discrete preservation of positive variables on interfaces, and at the same time to compute vacuum occurence or propagation of shock waves over a near-vacuum. A short section is also dedicated to the non-conservative hyperbolic equations arising within the setting of one-equation or two-equation turbulent compressible models. Many numerical tests confirm the capabilities of the scheme, and measuring the L 1 error norm in particular cases enables us to specify the actual rate of convergence.

Keywords

Shock Wave Euler Equation Error Norm Actual Rate Numerical Test 
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.

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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  • T. Gallouët
    • 1
  • J.-M. Hérard
    • 1
    • 2
  • N. Seguin
    • 1
  1. 1.Université de Provence, Centre de Mathématiques et d’Informatique, Laboratoire d’Analyse, Topologie et Probabilités - UMR CNRS 6632, MarseilleFrance
  2. 2.Électricité de France, Division Recherche et Développement, Département Mécanique des Fluides et Transferts Thermiques, ChatouFrance

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