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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Microscopic derivation of discrete hydrodynamics
Pep Español1, Jesús G Anero, Ignacio Zúñiga
1Dept. Fisica Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain. pep@fisfun.uned.es
The Journal of Chemical Physics
|January 12, 2010
Summary
This study derives discrete hydrodynamic equations using coarse-graining theory, offering a new method for discretizing Navier-Stokes equations on irregular grids. The approach ensures conservation laws and exact thermal fluctuation implementation.
Area of Science:
- Computational Physics
- Fluid Dynamics
- Statistical Mechanics
Background:
- Coarse-graining theory provides a bridge between microscopic dynamics and macroscopic descriptions.
- Discretization of fluid dynamics equations is crucial for numerical simulations.
- Navier-Stokes equations govern fluid motion but are challenging to solve analytically.
Purpose of the Study:
- To derive dynamic equations for discrete hydrodynamic variables using coarse-graining.
- To establish a connection between microscopic dynamics and discretization schemes for partial differential equations.
- To implement thermal fluctuations in a physically consistent manner.
Main Methods:
- Application of Zwanzig's projection operator formalism for coarse graining.
- Definition of hydrodynamic variables based on Delaunay triangulation.
- Microscopic derivation of discrete equations ensuring conservation laws.
Main Results:
- Development of discrete hydrodynamic equations equivalent to a Navier-Stokes discretization on irregular grids.
- Exact conservation of mass, momentum, and energy in the derived equations.
- Accurate implementation of thermal fluctuations satisfying the fluctuation-dissipation theorem.
Conclusions:
- The study demonstrates a novel microscopic approach to discretizing fluid dynamics.
- The method provides a rigorous foundation for computational fluid dynamics on irregular meshes.
- This work highlights the deep connection between coarse-graining and numerical methods for PDEs.
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