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

TL;DR

This paper introduces a Fokker-Planck-Poisson kinetic model for simulating multi-phase flows far from equilibrium, combining stochastic molecular forces with long-range attractions for efficient physics-based simulations.

Contribution

It develops a novel multi-phase particle method based on Fokker-Planck-Poisson equations, extending kinetic approaches to complex multi-phase phenomena.

Findings

Efficient simulation of multi-phase phenomena far from equilibrium.

Analysis of heat flux departure from Fourier's law in droplets.

Study of droplet growth during spinodal decomposition.

Abstract

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighboring phases, yet their closure far from the continuum needs to be modeled. 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 gasses [Phys. Fluids, 29 (12), 2017] and long-range interactions [J. Comput. Phys, 378, 2019]. It is on this background that the current work on Fokker-Planck-Poisson modeling of multi-phase phenomena is initiated. Molecular interactions are expressed via stochastic forces driven by the white noise, coupled with 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 workflow 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-gradient 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.