Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of compressible two-component flow, and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is -- at present -- no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method, and has been introduced recently for compressible one-component flow with phase transitions in [Magiera and Rohde, JCP. 469 (2022)]. To overcome the numerical complexity of the molecular-dynamics microscale model a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argon-methane mixtures in several space-dimensions. Up to our knowledge such compressible two-phase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

翻译：理解流体中相界面动力学需要关于界面微尺度过程的定量知识。本文考虑可压缩双组分流的尖锐界面运动，提出一种异质多尺度方法（HMM）以精确描述流场。该多尺度方法将连续尺度上的双曲型平衡律系统与微尺度层面的分子动力学模拟相结合。值得注意的是，由于目前尚不存在封闭的连续尺度模型，因此必须采用多尺度方法来计算界面动力学。基础HMM依赖于移动网格有限体积法，近期已在[Migiera and Rohde, JCP. 469 (2022)]中针对具有相变的可压缩单组分流提出。为克服分子动力学微尺度模型的数值复杂性，采用深度神经网络作为高效替代模型。最终将该方法应用于模拟氩-甲烷混合物在多个空间维度中的液滴动力学。据我们所知，此类考虑微尺度相变传输速率的可压缩两相动力学尚未被计算。