Geodesic
On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 31-37

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We study an explicit two-level symmetric (in space) finite-difference scheme for the multidimensional barotropic gas dynamics system of equations with quasi-gasdynamic regularization linearized at a constant solution (with an arbitrary velocity). A criterion and both necessary and sufficient conditions for the $L^2$-dissipativity of the solutions to the Cauchy problem for the scheme are derived by the spectral method. In them, the Courant number is uniformly bounded with respect to the Mach number.
Keywords: barotropic gas dynamics equations, quasi-gasdynamic system of equations, explicit two-level finite-difference scheme, stability. 
@article{DANMA_2020_492_a6,
     author = {A. A. Zlotnik and T. A. Lomonosov},
     title = {On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {31--37},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a6/}
}
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A. A. Zlotnik; T. A. Lomonosov. On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 31-37. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a6/