Open AccessOn L2-dissipativity of a linearized difference scheme on staggered meshes with a quasi-hydrodynamic regularization for 1D barotropic gas dynamics equations
Author(s) -
А. А. Злотник,
Т. А. Ломоносов
Publication year - 2021
Publication title -
preprint/preprinty ipm im. m.v. keldyša
Language(s) - English
Resource type - Journals
eISSN - 2071-2901
pISSN - 2071-2898
DOI - 10.20948/prepr-2021-72
Subject(s) - barotropic fluid , regularization (linguistics) , mathematics , mathematical analysis , linearization , viscosity , physics , nonlinear system , mechanics , thermodynamics , quantum mechanics , artificial intelligence , computer science
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 L 2 -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.