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Resummed Green-Kubo relations for a fluctuating fluid-particle model.
1Institut für Computeranwendungen, Universität Stuttgart Pfaffenwaldring 27, 70569 Stuttgart, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
Summary
A new stochastic fluid flow model achieves Galilean invariance through grid shifting, enhancing momentum transfer and transport coefficients. This method precisely determines collisional contributions and clarifies kinetic-collisional interactions.
Area of Science:
- Computational fluid dynamics
- Statistical mechanics
- Kinetic theory
Background:
- Stochastic models for fluid flow are essential for simulating complex systems.
- Ensuring Galilean invariance is crucial for the physical accuracy of fluid flow models.
- Transport coefficients quantify fluid behavior and are key parameters in fluid dynamics.
Purpose of the Study:
- To develop a Galilean invariant stochastic model for fluid flow.
- To investigate the impact of grid shifting on momentum transfer and transport coefficients.
- To exactly determine the collisional contribution to transport coefficients.
Main Methods:
- Introducing a random shift of the computational grid before collisions.
- Resumming Green-Kubo relations to derive transport coefficients.
- Analyzing correlation corrections and comparing with simulation data.
Main Results:
- The stochastic model is rendered Galilean invariant by the grid shifting procedure.
- Grid shifting accelerates momentum transfer, introducing a collisional contribution to transport coefficients.
- Exact expressions for transport coefficients were derived, showing no mixed kinetic-collisional contributions.
Conclusions:
- The proposed grid shifting method successfully achieves Galilean invariance in stochastic fluid flow models.
- This approach provides an exact method for determining collisional contributions to transport coefficients.
- The findings offer a more accurate theoretical framework for fluid flow simulations.