On Quasi-Gasdynamic System of Equations with General Equations of State and its Application

Abstract

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 extended 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 are derived for its relaxation summands. It is proved that under a condition on the heat source intensity, the non-negativity 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.

Keywords:

• quasi-gasdynamic equations
• general state equations
• the entropy balance equation
• Euler equations
• finite-difference methods

AMS Subject Classification::

• 76N15
• 76M20