Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme

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Abstract

Abstract: Monotonicity conditions for the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux are obtained. It is shown that the monotonicity of the CABARET scheme for Courant numbers r ∈ (0.5,1] does not ensure the complete decay of unstable strong discontinuities. For the CABARET scheme, a difference analogue of an entropy inequality is derived and a method is proposed ensuring the complete decay of unstable strong discontinuities in the difference solution for any Courant number at which the CABARET scheme is stable. Test computations illustrating these properties of the CABARET scheme are presented.

Original languageEnglish
Pages (from-to)950-966
Number of pages17
JournalComputational Mathematics and Mathematical Physics
Volume58
Issue number6
DOIs
Publication statusPublished - 1 Jun 2018

Keywords

  • difference analogue of entropy inequality
  • monotone CABARET scheme
  • scalar conservation law
  • strong discontinuity
  • CHANGING CHARACTERISTIC FIELD
  • EQUATIONS
  • MONOTONICITY
  • SYSTEMS
  • SHOCKS

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