Resummed Green-Kubo relations for a fluctuating fluid-particle model

TL;DR

This paper develops exact resummed Green-Kubo relations for a Galilean invariant stochastic fluid model, accurately capturing collisional contributions to transport coefficients and confirming the absence of mixed kinetic-collisional effects.

Contribution

It introduces a method to exactly determine collisional contributions to transport coefficients in a fluctuating fluid model using resummed Green-Kubo relations.

Findings

Collisional contributions can be exactly calculated.

No mixed kinetic-collisional contributions exist.

Explicit expressions match simulation data.

Abstract

A recently introduced stochastic model for fluid flow can be made Galilean invariant by introducing a random shift of the computational grid before collisions. This grid shifting procedure accelerates momentum transfer between cells and leads to a collisional contribution to transport coefficients. By resumming the Green-Kubo relations derived in a previous paper, it is shown that this collisional contribution to the transport coefficients can be determined exactly. The resummed Green-Kubo relations also show that there are no mixed kinetic-collisional contributions to the transport coefficients. The leading correlation corrections to the transport coefficients are discussed, and explicit expressions for the transport coefficients are presented and compared with simulation data.