Equilibrium calculation of transport coefficients for a fluid-particle model

TL;DR

This paper derives exact expressions for transport coefficients in a particle-based fluid model, revealing additional viscosity and thermal conductivity contributions, and discusses their implications for the model's applicability.

Contribution

It provides a detailed equilibrium calculation of transport coefficients for the Stochastic Rotation Dynamics model, including collisional contributions and their effects.

Findings

Collisional stress tensor is asymmetric, leading to extra viscosity.

Exact expressions for collisional contributions to transport coefficients are obtained.

Thermal conductivity contributions are significant at small mean free paths.

Abstract

A recently introduced particle-based model for fluid flow, called Stochastic Rotation Dynamics, can be made Galilean invariant by introducing a random shift of the computational grid before collisions. In this paper, it is shown how the Green-Kubo relations derived previously can be resummed to obtain exact expressions for the collisional contributions to the transport coefficients. It is also shown that the collisional contribution to the microscopic stress tensor is not symmetric, and that this leads to an additional viscosity. The resulting identification of the transport coefficients for the hydrodynamic modes is discussed in detail, and it is shown that this does not impose restrictions on the applicability of the model. The collisional contribution to the thermal conductivity, which becomes important for small mean free path and small average particle number per cell, is also derived.