Stochastic rotation dynamics. II. Transport coefficients, numerics, and long-time tails

Abstract

A discrete-time projection operation technique was used to derive the Green-Kubo relations for the transport coefficients of a recently introduced stochastic model for fluid dynamics in a previous paper (Part 1). The most important feature of the analysis was the incorporation of a new grid shifting procedure which was shown to guarantee Galilean invariance for arbitrary Mach number and temperature. This paper (Part 2) contains a detailed analysis of the transport coefficients of this model. An exact calculation of the first terms in the stress correlation function in the limit of infinite particle density is presented, which explicitly accounts for the cell structure introduced to define the collision environment. It is also shown that this cell structure can lead to additional contributions to the transport coefficients even at large mean free paths. Explicit expressions for all transport coefficients are derived and compared with simulation results. Long-time tails in the velocity, stress, and heat-flux autocorrelation functions are measured and shown to be in excellent agreement with the predictions of mode-coupling theory.