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

Area of Science:

• Fluid Dynamics
• Statistical Mechanics
• Computational Physics

Background:

• A novel stochastic model for fluid dynamics was introduced in Part 1.
• This model incorporates a grid shifting procedure ensuring Galilean invariance.

Purpose of the Study:

• To perform a detailed analysis of the transport coefficients within the stochastic fluid dynamics model.
• To derive explicit expressions for transport coefficients and compare them with simulation results.

Main Methods:

• Utilized a discrete-time projection operation technique to derive Green-Kubo relations.
• Performed exact calculations of stress correlation functions in the infinite particle density limit.
• Investigated the impact of cell structure on transport coefficients.

Main Results:

• Derived explicit expressions for all transport coefficients.
• Demonstrated additional contributions to transport coefficients due to cell structure, even at large mean free paths.
• Measured long-time tails in velocity, stress, and heat-flux autocorrelation functions.

Conclusions:

• The derived transport coefficients show excellent agreement with simulation results.
• Observed long-time tails align perfectly with predictions from mode-coupling theory.
• The stochastic model provides a robust framework for studying fluid dynamics transport phenomena.