A weighted particle scheme for Enskog-Vlasov equation to simulate spherical nano-droplets/bubbles

The Enskog-Vlasov equation has been proven successful in capturing the complex behaviour of fluids undergoing a phase change. However, its numerical solution is computationally demanding, and this has restricted the studies to one- and two-dimensional planar flows. In this work, a weighted particle scheme is developed for the numerical solution of the Enskog–Vlasov equation in spherically symmetric geometry. It is shown how weighted schemes designed for the Boltzmann equation can be extended to cope with the non-local structure of the Enskog collision integral, and a compact expression of the mean force field is determined using the shell theorem. As an application, the growth rates of nano-droplets/bubbles in the bulk of a homogeneous metastable vapour/liquid are evaluated in a wide range of supersaturation ratios that was not possible until now due to the high computational cost required by alternate approaches. The proposed scheme significantly broadens the range of problems that can be investigated via the Enskog-Vlasov equation, and it is a stepping stone towards the simulation of general three-dimensional liquid-vapour flows.