Reflection and Refraction of Waves Across an Interface of Two-phase Flow

We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase transition. The refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase interface. We apply the characteristic method and hodograph transform of Riemann to reduce the nonlinear PDEs to a concise form. Specially for the case of incident rarefaction wave, reduced linear equations are convenient to solve by Laplace transform. Then an integral formula in wave interaction region is derived in this paper, instead of the hypergeometric functions solutions for non-isothermal polytropic gases. It is also observed that when incident waves travel from the vapor phase to the liquid phase, the refracted waves must be accelerated and move forward.