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<p>We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions applied to the Euler equations of compressible gas dynamics. We work under a physically-reasonable assumption that a fluid is out of vacuum and has a bounded energy. Two key novelties of our method are i) entropy is treated as one of the main field quantities and ii) the total energy conservation is a consequence of compatible discretization and application of the Abgrall flux.</p>

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Convergence of a hyperbolic thermodynamically compatible finite volume scheme for the Euler equations

  • 期刊论文

  • 发表日期：

    2025年12月20日

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  • Michael Dumbser,
  • Mária Lukáčová-Medvid’ová,
  • Andrea Thomann

摘要

We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions applied to the Euler equations of compressible gas dynamics. We work under a physically-reasonable assumption that a fluid is out of vacuum and has a bounded energy. Two key novelties of our method are i) entropy is treated as one of the main field quantities and ii) the total energy conservation is a consequence of compatible discretization and application of the Abgrall flux.