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Regular version of the site

Book chapter

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.

In book

Edited by: S. Pinelas, T. Caraballo, P. Kloeden et al. Vol. 230. Cham: Springer, 2018.