Study of Entropy Properties of a Linearized Version of Godunov’s Method

S. K. Godunov, V. V. Denisenko, D. V. Klyuchinskii, S. V. Fortova, V. V. Shepelev

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finite-difference formulation with the help of the simplest linearized version of the classical Godunov scheme. It is experimentally shown that this version guarantees an entropy nondecrease. As a result, the growth of entropy on shock waves can be simulated without using any correction terms or additional conditions.

Original languageEnglish
Pages (from-to)628-640
Number of pages13
JournalComputational Mathematics and Mathematical Physics
Volume60
Issue number4
DOIs
Publication statusPublished - 1 Apr 2020

Keywords

  • discontinuous solutions
  • entropy nondecrease
  • gas dynamics equations
  • Godunov’s scheme
  • Riemann problem
  • shock waves
  • weak solution

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.03 PHYSICAL SCIENCES AND ASTRONOMY

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