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On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations. (English) Zbl 1407.76106
Pinelas, Sandra (ed.) et al., Differential and difference equations with applications. ICDDEA, Amadora, Portugal, June 5–9, 2017. Cham: Springer. Springer Proc. Math. Stat. 230, 635-647 (2018).
Summary: 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.
For the entire collection see [Zbl 1398.35005].

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 76N15 Gas dynamics, general
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