Fokker-Planck-Poisson kinetics: multi-phase flow beyond equilibrium

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighbouring phases, yet their closure far from the continuum needs to be modelled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. This approach is built closely upon the previous studies on the kinetic method development for dense gases [Phys. Fluids, vol. 29 (12), 2017] and long-range interactions [J. Comput. Phys., vol. 378, 2019]. It is on this background that the current work on Fokker-Planck-Poisson modelling of multi-phase phenomena is initiated. Molecular interactions are expressed via stochastic forces driven by the white noise, coupled to the long-range attractions. The former is local and pursues diffusive approximation of molecular collisions, whereas the latter takes a global feature owing to mean-field forces. The obtained Fokker-Planck-Poisson combination provides an efficient work flow for physics-driven simulations suitable for multi-phase phenomena far from the equilibrium. Besides highlighting the computational efficiency of the method, various archetypical and complex problems ranging from inverted temperature gradients between droplets to spinodal decomposition are explored. Detailed discussions are provided on different characteristics of the droplets dispersed in low/high density background gases; including the departure of heat fluxes from Fourier's law as well as droplets growth in spinodal phases.