A. A. Zlotnik, “Conditions for dissipativity of an explicit finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations”, Dokl. RAN. Math. Inf. Proc. Upr., 2022, Volume 505,Pages <nobr>30

This article is cited in 2 papers

MATHEMATICS

Conditions for dissipativity of an explicit finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations

A. A. Zlotnik^ab

^a National Research University "Higher School of Economics", Moscow, Russia
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia

Abstract: We study an explicit two-level finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations. For an initial-boundary value problem on a nonuniform rectangular mesh, sufficient conditions of Courant-type for $L^2$-dissipativity are derived for the first time by applying the energy method. For the Cauchy problem on a uniform mesh, both necessary and sufficient conditions for $L^2$-dissipativity in the spectral method are improved. A new form of specifying the relaxation parameter is indicated which guarantees that the Courant-type number is uniformly bounded from above and below with respect to both the mesh and the Mach number.

Keywords: gas dynamics equations, quasi-gasdynamic system of equations, linearization, explicit finite-difference scheme, dissipativity.

UDC: 519.633.8+517.958:533.7

Presented: B. N. Chetverushkin
Received: 16.03.2022
Revised: 23.05.2022
Accepted: 03.06.2022

DOI: 10.31857/S2686954322040191