In the present study,a compressible multi-scale flow solver is described,based on the discontinuous Galerkin(DG)spectral element method.To incorporate multiphase effects,the phase interface is tracked via a level-set method embedded in the discontinuous Galerkin method,which allows an accurate curvature calculation.The interface is resolved sharply using a ghost fluid approach.The advantage of the DG method of allowing discontinuities at element faces is utilized such that the interface position coincides with element faces; the solution is then obtained by numerical fluxes,similar to finite volume methods.Since a high order approximation allows large grid cells,the solution is refined locally at the interface position.Here,we switch to an equidistant finite volume grid to improve robustness and locality.Jump conditions for the state variables are provided by a newly developed approximative Riemann solver.To incorporate phase transition effects,an additional undercompressive wave is introduced into the classical Riemann wave pattern.Therefore,the well-known HLL Riemann solver is extended to include an evaporation wave.The solver is named HLLP,where the P refers to the additional phase resolving wave.For both phases,left and right of the phase interface,approximative fluxes are provided.The resolution of the evaporation wave requires an additional estimate for the mass flux such that the thermodynamic laws are fulfilled and a unique solution is obtained.The phase transfer mass flux is estimated by the evaporation model by Schrage.We show results for the extension of the HLLP Riemann solver towards multicomponent problems,using appropriate jump conditions for the vapour mass fraction and the Peng-Robinson EOS with Van-der-Waals mixing rules.The solver is validated for the case of a single component droplet evaporating in an inert carrier gas.