Author:
Zlotnik A. A.,Chetverushkin B. N.
Abstract
Abstract
We study difference schemes associated with a simplified linearized multidimensional
hyperbolic quasi-gasdynamic system of differential equations. It is shown that an explicit two-level
vector difference scheme with flux relaxation for a second-order hyperbolic equation with variable
coefficients that is a perturbation of the transport equation with a parameter multiplying the
highest derivatives can be reduced to an explicit three-level difference scheme. In the case of
constant coefficients, the spectral condition for the time-uniform stability of this explicit
three-level difference scheme is analyzed, and both sufficient and necessary conditions for this
condition to hold are derived, in particular, in the form of Courant type conditions on the ratio of
temporal and spatial steps.
Subject
General Mathematics,Analysis
Reference17 articles.
1. Chetverushkin, B.N., Hyperbolic quasi-gasdynamic system, Math. Models Comput. Simul., 2018, vol. 10,
pp. 588–600.
2. Chetverushkin, B.N., Kinetic Schemes and
Quasi-Gasdynamic System of Equations, Barcelona: Int. Center Numer. Methods
Eng. (CIMNE), 2008.
3. Elizarova, T.G., Quasi-Gas Dynamic
Equations, Dordrecht: Springer, 2009.
4. Zlotnik, A.A. and Chetverushkin, B.N., Parabolicity of the quasi-gasdynamic
system of equations, its hyperbolic second-order modification, and the stability of small
perturbations for them, Comput. Math. Math. Phys.,
2008, vol. 48, no. 3, pp. 420–446.
5. Chetverushkin, B.N. and Zlotnik, A.A., On some properties of
multidimensional hyperbolic quasi-gasdynamic systems of equations, Russ. J. Math. Phys., 2017, vol. 24, no. 3,
pp. 299–309.