Accelerating the Monte Carlo simulation of the Enskog equation for multiscale dense gas flows

Abstract

A general synthetic iterative scheme is proposed to solve the Enskog equation within a Monte Carlo framework. The method demonstrates rapid convergence by reducing intermediate Monte Carlo evolution and preserves the asymptotic-preserving property, enabling spatial cell sizes much larger than the mean free path in near-continuum flows. This is realized through mesoscopic-macroscopic two-way coupling: the mesoscopic Monte Carlo simulation provides high-order constitutive relations to close the moment (synthetic) equation, while the macroscopic synthetic equation, once solved toward steady state, directs the evolution of simulation particles in the Monte Carlo method. The accuracy of the proposed general synthetic iterative scheme is verified through one-dimensional normal shock wave and planar Fourier heat transfer problems, while its fast-converging and asymptotic-preserving properties are demonstrated in the force-driven Poiseuille flow and two-dimensional hypersonic cylinder flow and low-speed porous media flow, where the simulation time is reduced by several orders of magnitude in near-continuum flows. With the proposed method, a brief analysis is conducted on the role of the adsorption layer in porous media flow, mimicking shale gas extraction.