Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows

Abstract

We consider the dynamics of a compressible fluid exhibiting phase transitions between a liquid and a vapour phase. As the basic mathematical model we use the Euler equations for a sharp interface approach and local and global versions of the Navier–Stokes–Korteweg equations for the diffuse interface approach. The mathematical models are discussed and we introduce discretization methods for both approaches. Finally numerical simulations in one and two space dimensions are presented.