A HLL-type Riemann solver for two-phase flow with surface forces and phase transitions

We present a new HLL-type approximate Riemann solver for a compressible two-phase flow model with phase transition and surface forces such as surface tension or electric forces. The solver is obtained following the main ideas of the HLL-approach. Due to the nonlinearity in the kinetic relation driving the phase transition, this solver involves the solution of one single nonlinear equation, contrary to a single-phase HLL-type solver, where no nonlinear equations have to be solved. We present some illustrative numerical examples to show the performance and accuracy of the new solver, comparing it to the relaxation Riemann solver from the literature as well as to the two-shock approximation, which is the most accurate interface Riemann solver currently available for the present situation, but suffers from high computational costs.