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Mesoscopic approach to inviscid gas dynamics with thermal lag

A phenomenological model for thermal relaxation and wave propagation in ideal polyatomic gases is developed by introducing a dynamical non‐equilibrium temperature. The system of equations governing the evolution of the gas is derived and the speeds of propagation of thermo‐mechanical disturbances together with the Rankine‐Hugoniot jump conditions for shock waves are calculated. The hyperbolic theories of heat propagation in incompressible fluids and rigid solids are recovered as particular cases. For rigid solids, the well posedness of the Cauchy problem is proved by a classical method.