Shock Structure in a Two-phase Isothermal Euler Model

Abstract

We have performed a traveling wave analysis of a two phase isothermal Euler model to exhibit the inner structure of shock waves in two-phase flows. In the model studied in this work, the dissipative regularizing term is not of viscous type but instead comes from relaxation phenomena toward equilibrium between the phases. This gives an unusual structure to the diffusion tensor where dissipative terms appear only in the mass conservation equations. We show that this implies that the mass fractions are not constant inside the shock although the Rankine-Hugoniot relations give a zero jump of the mass fraction through the discontinuities. We also show that there exists a critical speed for the traveling waves above which no C 1 solutions exist. Nevertheless for this case, it is possible to construct traveling solutions involving single phase shocks