Abstract: 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 the 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 (MD) 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 the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469:111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argonmethane mixtures in several space dimensions. To our knowledge, such compressible twophase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

Key words: Phase transition, Hyperbolic balance laws for multi-component fluids, Multiscale modeling, Moving-mesh methods, Deep neural networks