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

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.

12 pages, 4 figures, to appear in PRL. Published version is shortened to meet the page limit

References in corpus (3)

• Kinetic boundary conditions in the lattice Boltzmann method
• Minimal entropic kinetic models for simulating hydrodynamics
• Consistent Lattice Boltzmann Method

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