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

S. Ansumali·I. V. Karlin·S. Arcidiacono·A. Abbas·N. I. Prasianakis
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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.

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S. Ansumali, I. V. Karlin, S. Arcidiacono, A. Abbas, N. I. Prasianakis. 2007-03-16. Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy. https://doi.org/10.1103/physrevlett.98.124502

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