Contact Discontinuity Capturing Schemes for Linear Advection and Compressible Gas Dynamics

  • Authors:

  • Bruno Despré/s;Fré/dé/ric Lagoutiè/re

  • Affiliations:

  • Laboratoire d'analyse numé/rique, Université/ P. et M. Curie, 4, place Jussieu, 75005 Paris, France/ and Commissariat à/ l'É/nergie Atomique, CEA/DIF, BP12, 91680 Bruyè/res-le- ...;Laboratoire d'analyse numé/rique, Université/ P. et M. Curie, 4, place Jussieu, 75005 Paris, France. lagoutie@ann.jussieu.fr

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2002

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Abstract

We present a non-diffusive and contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to the Ultra-Bee limiter of [24], [29]. We prove for the Ultra-Bee scheme a property of exact advection for a large set of piecewise constant functions. We prove that the numerical error is uniformly bounded in time for such prepared (i.e., piecewise constant) initial data, and state a conjecture of non-diffusion at infinite time, based on some local over-compressivity of the scheme, for general initial data. We generalize the scheme to compressible gas dynamics and present some numerical results.