Liquid Vapor Phase Transitions: Modeling, Riemann Solvers and Computation

Abstract

The numerical approximation of liquid vapor flows within the compressible regime is a challenging task because complex physical effects at the phase interfaces govern the global flow behavior. We develop a sharp interface approach which treats the phase boundary like a shock wave discontinuity and takes capillarity effects into account. The approach relies on the solution of Riemann problems across the interface that separates the liquid and the vapor phase. The Riemann solution accounts for the relevant physics by enforcing appropriate jump conditions at the phase boundary. A wide variety of interface effects can be handled in a thermodynamically consistent way. This includes surface tension, as well as, mass and energy transfer by phase transition. Moreover, the local normal speed of the interface, which is needed to calculate the time evolution of the phase boundary, is given by the Riemann solution. The focus of this work is the development of isothermal and non-isothermal two-phase Riemann solvers for the sharp interface approach. To verify the solvers with respect to numerical and thermodynamic requirements, one-dimensional and radially symmetric problems are studied. Furthermore, the Riemann solvers and the sharp interface approach are successfully validated against shock tube experiments of real fluids (alkanes).