Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws

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Abstract

A method is proposed for constructing a CABARET scheme that approximates a hyperbolic system of conservation laws that cannot be written in the form of invariants. This technique is based on the method of quasi-invariants and additional flux correction, which ensures monotonization of the difference solution in calculating discontinuous solutions with shock waves and contact discontinuities. As an example, a system of conservation laws for nonisentropic gas dynamics with a polytropic equation of state is considered. Test calculations of the Blast Wave initial-boundary value problem showed that the proposed scheme suppresses nonphysical oscillations leading to the instability of the difference solution in the case when the CABARET scheme is used without additional flux correction.

Original languageEnglish
Pages (from-to)369-373
Number of pages5
JournalDoklady Mathematics
Volume104
Issue number3
DOIs
Publication statusPublished - Nov 2021

Keywords

  • Blast Wave problem
  • CABARET scheme
  • equations of gas dynamics
  • quasi-invariants method

OECD FOS+WOS

  • 1.01 MATHEMATICS

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