Extended thermodynamics of dense gases in the presence of dynamic pressure

Extended thermodynamics (ET) developed up to now fails when a gas is very dense and is composed of molecules with small internal degrees of freedom because the condition of convexity (stability) is violated. The aim of this paper is to explore a possible approach to construct an ET theory that is valid for any dense gas with the condition that it reduces to the usual ET theory when a gas is sufficiently rarefied. We restrict our study, for simplicity, within the simplest case in which the dissipation is only due to the dynamic pressure. Therefore the basic system of equations is the simplest variant of the Euler system, that is, the system composed of the equations for the conservation laws and an equation for the dynamic pressure (6-field theory).