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.

翻译：我们提出了一个精确且数学一致的两相流动扩散界面模型公式化，该模型涉及快速蒸发。所提出的模型解决了密度场存在数量级不连续性带来的挑战，这导致液-气界面处产生高速度和压力跳跃，以及动态变化的界面拓扑结构。为此，我们将不可压缩Navier-Stokes求解器与守恒型水平集公式化以及间断的正则化（即扩散）表示相结合，集成到一个无矩阵自适应有限元框架中。成果体现在三个方面：第一，本文通过从液相或气相外推速度，为扩散界面区域中的水平集输运速度提出了数学一致的定义，与局部速度评估相比，这种定义在预测蒸发质量及由此产生的界面动力学方面表现出更高的精度，尤其对于高度弯曲的界面。第二，我们表明，准确预测蒸发引起的压力跳跃需要在界面处进行一致（即倒数形式）的密度插值，这满足局部质量守恒。第三，将用于蒸发的扩散界面模型与黏性流动的标准Stokes型本构关系相结合，会导致扩散界面区域出现显著的压力伪影。为缓解这一问题，我们对此类本构模型类型提出了一种修正方案。通过选定的分析和数值示例，上述特性得到了验证。所提出的模型有望为热多相流（例如金属激光粉末床熔融）中熔体-蒸气相互作用的模拟预测提供新的见解。