Discrete hydrodynamics near solid planar walls

Area of Science:

• Fluid dynamics
• Computational physics
• Statistical mechanics

Background:

• Understanding fluid behavior in confined geometries is crucial for various scientific and engineering applications.
• Traditional methods often rely on continuum equations and boundary conditions, which may not fully capture microscopic interactions.

Purpose of the Study:

• To derive discrete hydrodynamic equations for confined fluids using the projection operator technique.
• To incorporate wall interactions directly into the equations of motion through impenetrability and friction forces.
• To provide microscopic expressions for transport coefficients within the discrete framework.

Main Methods:

• Projection operator technique to derive equations of motion.
• Assumption of translational invariance along wall-tangent directions.
• Formulation of discrete hydrodynamic equations including wall interaction forces.

Main Results:

• Derived time-dependent average equations for discrete mass and momentum densities.
• Demonstrated that shear flow and sound propagation perpendicular to walls are described by these equations.
• Provided microscopic expressions for transport coefficients.
• Showed equivalence to a Petrov-Galerkin finite-element discretization of continuum equations under specific conditions.

Conclusions:

• The derived discrete hydrodynamic equations offer a novel approach to modeling confined fluids.
• Wall interactions are effectively modeled through forces, bypassing traditional boundary conditions.
• The framework provides a link between microscopic properties and macroscopic fluid behavior in confined systems.