A phase-field model for flows with phase transition

Abstract

There are many mathematical models for describing compressible or incompressible flows with phase transition. In this contribution, we will focus on the Navier–Stokes–Korteweg model [12] (Appl Math Comput 272, part 2, 309–335, 2016) and a phase-field model: The compressible Navier–Stokes–Allen–Cahn model (NSAC) is able to model compressible two-phase flows including surface tension effects and phase transitions. In this contribution, we will present a discontinuous Galerkin scheme for the NSAC model. The scheme is designed to fulfill a discrete version of the free energy inequality, which is the second law of thermodynamics in the isothermal case. For situations near the thermodynamic equilibrium, this property suppresses so-called parasitic currents, which are unphysical velocity fields near the phase boundary.