DOI: 10.1209/epl/i2003-00496-6
Europhys. Lett., 63 (6) , pp. 798-804 (2003)

Minimal entropic kinetic models for hydrodynamics

S. Ansumali, I. V. Karlin and H. C. Öttinger

ETH-Zürich, Department of Materials, Institute of Polymers ETH-Zentrum - Sonneggstr. 3, ML J 19, CH-8092 Zürich, Switzerland

(Received 20 January 2003; accepted in final form 10 July 2003)

Abstract
We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A new discrete velocity model is proposed for the simulation of the Navier-Stokes-Fourier equation and is tested in the setup of Taylor vortex flow. A simple analytical procedure for constructing the equilibrium for thermal hydrodynamics is established. For the lattice Boltzmann method of isothermal hydrodynamics, the explicit analytical form of the equilibrium distribution is presented. This results in an entropic version of the isothermal lattice Boltzmann method with the simplicity and computational efficiency of the standard lattice Boltzmann model.

PACS
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
47.11.+j - Computational methods in fluid dynamics.
51.10.+y - Kinetic and transport theory of gases.

© EDP Sciences 2003