Volume 63, Number 6, September 2003
|Page(s)||798 - 804|
|Published online||01 November 2003|
Minimal entropic kinetic models for hydrodynamics
ETH-Zürich, Department of Materials, Institute of Polymers ETH-Zentrum - Sonneggstr. 3, ML J 19, CH-8092 Zürich, Switzerland
Accepted: 10 July 2003
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
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