Phys. Rev. Lett. 98, 124502 (2007) - Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy

Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy

S. Ansumali, I. V. Karlin, S. Arcidiacono, A. Abbas, and N. I. Prasianakis

Phys. Rev. Lett. 98, 124502 – Published 22 March 2007

Abstract

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

Received 26 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.124502

©2007 American Physical Society

Authors & Affiliations

School of Chemical and Biomedical Engineering, Nanyang Technological University, 639798 Singapore, Singapore

Aerothermochemistry and Combustion Systems Lab, ETH Zurich, 8092 Zurich, Switzerland

Paul Scherrer Institute, Combustion Research, 5232 Villigen PSI, Switzerland

School of Chemical and Biomedical Engineering, Nanyang Technological University, 639798 Singapore, Singapore

N. I. Prasianakis

Aerothermochemistry and Combustion Systems Lab, ETH Zurich, CH-8092 Zurich, Switzerland

^*Corresponding author.

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Issue

Vol. 98, Iss. 12 — 23 March 2007

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