  We present accurate and mathematically consistent formulations of a
diffuse-interface model for two-phase flow problems involving rapid
evaporation. The model addresses challenges including discontinuities in the
density field by several orders of magnitude, leading to high velocity and
pressure jumps across the liquid-vapor interface, along with dynamically
changing interface topologies. To this end, we integrate an incompressible
Navier--Stokes solver combined with a conservative level-set formulation and a
regularized, i.e., diffuse, representation of discontinuities into a
matrix-free adaptive finite element framework. The achievements are three-fold:
First, this work proposes mathematically consistent definitions for the
level-set transport velocity in the diffuse interface region by extrapolating
the velocity from the liquid or gas phase, which exhibit superior prediction
accuracy for the evaporated mass and the resulting interface dynamics compared
to a local velocity evaluation, especially for highly curved interfaces.
Second, we show that accurate prediction of the evaporation-induced pressure
jump requires a consistent, namely a reciprocal, density interpolation across
the interface, which satisfies local mass conservation. Third, the combination
of diffuse interface models for evaporation with standard Stokes-type
constitutive relations for viscous flows leads to significant pressure
artifacts in the diffuse interface region. To mitigate these, we propose a
modification for such constitutive model types. Through selected analytical and
numerical examples, the aforementioned properties are validated. The presented
model promises new insights in simulation-based prediction of melt-vapor
interactions in thermal multiphase flows such as in laser-based powder bed
fusion of metals.
