On dissipativity of linearized 1d quasi-gasdynamic system of equations and its difference approximation for general equations of state

Lobachevskii Journal of Mathematics. 2025. Vol. 46. No. 11. P. 5718–5731.

A. Zlotnik, T. Lomonosov

We deal with the 1D quasi-gasdynamic (QGD) system of equations and a two-level explicit in time and three-point symmetric in space conservative difference scheme that approximates it, in the case of general equations of state.
Both the QGD system and scheme are linearized at any constant background solution (with non-zero or zero velocity). Matrices of their convective and dissipative terms are the same, and after respective scaling, they both become symmetric and depend mainly on the background ``signed'' Mach number and the ratio of the specific heats as well as the QGD parameters. Moreover, their form is almost the same as in the previously studied basic particular case of the perfect polytropic gas. This allows us to extend results on $L^2$-dissipativity of the QGD system and the scheme to the general case.
 

Keywords: linearization, 1D gas dynamics equations, quasi-gasdynamic regularization, explicit difference scheme, general equations of state, $L^2$-dissipativity