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October 14, 2026
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On Quasi-Gasdynamic System of Equations with General Equations of State and its Application

Mathematical Modelling and Analysis. 2011. Vol. 16. No. 4. P. 509–526.
Zlotnik A., Gavrilin V.

A quasi-gasdynamic system of equations with a mass force and a heat source is well known in the case of the perfect polytropic gas. In the paper, the system is generalized to the case of general equations of gas state satisfying thermodynamic stability conditions. The entropy balance equation is studied. The validity of the non-negativity property is algebraically analyzed for the entropy production. Two different forms of writing are derived for its relaxation summands. Under a condition on the heat source intensity, the property is valid.

An application to one-dimensional Euler real gas dynamics equations is given. A two-level explicit symmetric in space finite-difference scheme is constructed. The scheme is tested in the cases of the stiffened gas and the Van der Waals gas equations of state.

Priority areas: mathematics
Language: English
Full text
DOI
Keywords: уравнение баланса энтропииquasi-gasdynamic equationsgeneral state equationsthe entropy balance equationEuler equationsfinite-difference methodsквазигазодинамические уравненияобщие уравнения состоянияуравнения Эйлераразностные методы
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