Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy

TL;DR

This paper presents an exact solution to the nonlinear lattice Boltzmann hierarchy in stationary Couette flow at finite Knudsen numbers, demonstrating the hierarchy's potential to accurately approximate kinetic theory.

Contribution

It introduces a new method combining moments and boundary conditions to derive closed-form solutions for all moments in the LB hierarchy.

Findings

Exact solutions at finite Knudsen numbers.

LB hierarchy with larger velocity sets improves kinetic theory approximation.

Convergence indicates the hierarchy's effectiveness.

Abstract

Exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at non-vanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables to derive closed-form solutions for all higher-order moments. Convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.