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Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor uid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost uid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions sharply, i. e., without articial smearing in the physically irrelevant elliptic region. Numerical experiments demonstrate the reliability of the method.

The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques