SHOCK STRUCTURE IN A HYPERBOLIC MODEL OF BINARY MIXTURE OF NON-REACTING GASES

In this paper the problem of shock structure in binary gas mixture is studied with assumption that temperatures of the constituents may not be equal. Mathematical model is developed within the context of extended thermodynamics leading to a hyperbolic system of quasi-linear partial differential equations. Classical Euler's system of gas dynamics equations appears to be an equilibrium subsystem of the mixture system. Due to the presence of dissipative terms discontinuous shock-wave solution is smoothed out to a continuous shock structure (profile) connecting two equilibrium states. By assuming the shock profile in the form of plane traveling wave a set of ordinary differential equations is derived from the complete set of balance laws. Numerical study revealed that there exists a smooth solution to the problem for shock speeds greater than the highest characteristic speed of the equilibrium subsystem. This solution confirms that mass difference is the main cause for the difference of temperatures of the constituents. Moreover, nonlinear form of source terms, obtained through the use of entropy principle, appear to be crucial for the problem in question since the intermediate states of the system are driven far from equilibrium.