Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules

TL;DR

This paper presents a theoretical and numerical analysis of transport coefficients in a particle-based fluid model with velocity-dependent collision rules, including derivations for self-diffusion and shear viscosity.

Contribution

It develops a general scheme to derive transport coefficients for biased, velocity-dependent collision rules in particle-based fluid models, with analytic expressions and validation.

Findings

Analytic expressions for self-diffusion and shear viscosity are derived.

Good agreement between theory and numerical results across different mean free paths.

Viscosity scales with the square root of temperature, matching real gas behavior.

Abstract

Detailed calculations of the transport coefficients of a recently introduced particle-based model for fluid dynamics with a non-ideal equation of state are presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are exactly conserved locally. A general scheme to derive transport coefficients for such biased, velocity dependent collision rules is developed. Analytic expressions for the self-diffusion coefficient and the shear viscosity are obtained, and very good agreement is found with numerical results at small and large mean free paths. The viscosity turns out to be proportional to the square root of temperature, as in a real gas. In addition, the theoretical framework is applied to a two-component version of the model, and expressions for the viscosity and the difference in diffusion of the two species are given.