Fully Resolved Compressible Two-Phase Flow: Modelling, Analytical and Numerical Issues

Mathematical models for compressible two-phase flow of homogeneous fluids that occur in a liquid and a vapour phase can be classified as either belonging to the class of sharp interface models or to the class of diffuse interface models. Sharp interface models display the phase boundary as a sharp front separating two bulk model domains while diffuse interface models consist of a single model on the complete domain of interest such that phase boundaries are represented as transition zones. This contribution is devoted to a self-consistent introduction to both model classes.Sharp interface models are analyzed within the theory of hyperbolic conservation laws with special focus on the Riemann problem. Based on the thermodynamically consistent solution of the Riemann problem a multidimensional finite volume method is introduced. For the associated diffuse interface ansatz the focus is on Navier–Stokes–Korteweg-type models. Several new variants are introduced which enable in particular thermodynamically consistent and asymptotically-preserving numerical discretizations. For all models it is assumed that the relevant spatial scale corresponds to fully resolved phase boundaries.