Dynamic correlations in stochastic rotation dynamics.

The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for stochastic rotation dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for the longitudinal transport coefficients such as thermal diffusivity and bulk viscosity. The results are in good agreement with earlier numerical and theoretical results, and it is shown for the first time that the bulk viscosity is indeed zero for this algorithm. In addition, corrections to the self-diffusion coefficient and shear viscosity arising from the breakdown of the molecular chaos approximation at small mean free paths are analyzed. In addition to deriving the form of the leading correlation corrections to these transport coefficients, the probabilities that two and three particles remain collision partners for consecutive time steps are derived analytically in the limit of small mean free path. The results of this paper verify that we have an excellent understanding of the SRD algorithm at the kinetic level and that analytic expressions for the transport coefficients derived elsewhere do indeed provide a very accurate description of the SRD fluid.

Equilibrium calculation of transport coefficients for a fluid-particle model.

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.

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

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.

Transport coefficients for stochastic rotation dynamics in three dimensions.

Explicit expressions for the transport coefficients of a recently introduced stochastic model for simulating fluctuating fluid dynamics are derived in three dimensions by means of Green-Kubo relations and simple kinetic arguments. The results are shown to be in excellent agreement with simulation data. Two collision rules are considered and their computational efficiency is compared.

Stochastic rotation dynamics. I. Formalism, Galilean invariance, and Green-Kubo relations.

A detailed analytical and numerical analysis of a recently introduced stochastic model for fluid dynamics with continuous velocities and efficient multi-particle collisions is presented. It is shown how full Galilean invariance can be achieved for arbitrary Mach numbers and how other low temperature anomalies can be removed. The relaxation towards thermal equilibrium is investigated numerically, and the relaxation time is measured. Equations of motions for the correlation functions of coarse-grained hydrodynamic variables are derived using a discrete-time projection operator technique, and the Green-Kubo relations for all relevant transport coefficients are given. In the following paper (Part 2), analytic expressions for the transport coefficients are derived and compared with simulation results. Long-time tails in the velocity and stress autocorrelation functions are measured and shown to be in good agreement with previous mode-coupling theories for continuous systems.

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

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.

Stochastic rotation dynamics: a Galilean-invariant mesoscopic model for fluid flow.

A recently introduced stochastic model for fluid dynamics with continuous velocities and efficient multiparticle collisions is investigated, and it is shown how full Galilean-invariance can be achieved for arbitrary Mach numbers. Analytic expressions for the viscosity and diffusion constant are also derived and compared with simulation results. Long-time tails in the velocity and stress autocorrelation functions are measured.