On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations

P. 635–647.

Zlotnik A., Lomonosov T.

We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in $L^2$ for the corresponding initial-value problem on the whole line. The criterion is essentially narrower than the necessary condition and wider than a sufficient one obtained recently in a particular case; moreover, it corresponds most well to numerical results for the original gas dynamics system.

Keywords: газовая динамика, баротропная квазигазодинамическая система уравнений, gas dynamics, Критерий устойчивости, barotropic quasi-gas dynamics system of equations, stability criterion, explicit finite-difference scheme, weak conservativeness, явная разностная схема, слабая консервативность

Publication based on the results of: Modern context of decision making and data analysis methods: human factor, uncertainty, risks, network models, big data (2018)

In book

Differential and Difference Equations with Applications

Vol. 230. , Springer, 2018.