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

Phys. Rev. Lett. 98, 124502 (2007) 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.