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KIAM Preprint № 72, Moscow, 2021
Authors: Zlotnik A.A., Lomonosov T.A.
On L2-dissipativity of a linearized difference scheme on staggered meshes with a quasi-hydrodynamic regularization for 1D barotropic gas dynamics equations
Abstract:
We study an explicit two-level finite difference scheme on staggered meshes, with a quasi-hydrodynamic regularization, for 1D barotropic gas dynamics equations. We derive necessary conditions and sufficient conditions close to each other for L2-dissipativity of solutions to the Cauchy problem for its linearization on a constant solution, for any background Mach number M. We apply the spectral approach and analyze matrix inequalities containing symbols of symmetric matrices of convective and regularizing terms. We consider the cases where either the artificial viscosity coefficient or the physical viscosity one is used. A comparison with the spectral von Neumann condition is also given for M=0.
Keywords:
dissipativity, linearized scheme, staggered meshes, regularization, 1D barotropic gas dynamics equations
Publication language: russian,  pages: 27
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Zlotnik Alexander Anatolievich,  orcid.org/0000-0003-2440-2816,  Higher School of Economics University; KIAM RAS
  • Lomonosov Timofey Alexandrovich,  orcid.org/0000-0002-3262-5772,  Higher School of Economics University