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arXiv · 1803.09899

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

A. Zlotnik·T. Lomonosov
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Abstract

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.

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A. Zlotnik, T. Lomonosov. 2018-03-27. On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations. https://doi.org/10.1007/978-3-319-75647-9_49

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