On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance
The one-dimensional quasi-gasdynamic system of equations in the form of mass, momentum, and total energy conservation laws with general gas equations of state is considered. A family of three-point symmetric spatial discretizations of this system is studied for which the internal energy equation has a suitable form (without imbalance terms). An entropy balance equation is derived, and the influence exerted by the choice of discretizations of various terms on the form of difference imbalance terms in this equation is determined. Special discretizations are presented for which the corresponding nondivergence imbalance terms are zero. The Euler system of equations is solved numerically in the cases of a perfect polytropic gas, stiffened gas, and the van der Waals equations of state.