Non-hydrodynamic modes and general equations of state in lattice
Boltzmann equations
P. J. Dellar (2006) Non-hydrodynamic modes and general
equations of state in lattice Boltzmann equations Physica
A 326, 132-138
doi:10.1016/j.physa.2005.09.012
Reprint as Adobe PDF (252K)
Abstract
The lattice Boltzmann equation is commonly used to simulate fluids with
isothermal equations of state in a weakly compressible limit, and
intended to approximate solutions of the incompressible Navier--Stokes
equations. Due to symmetry requirements there are usually more degrees
of freedom in the equilibrium distributions than there are constraints
imposed by the need to recover the Navier--Stokes equations in a slowly
varying limit. We construct equilibria for general barotropic fluids,
where pressure depends only upon density, using the two dimensional,
nine velocity (D2Q9) and one dimensional, five velocity (D1Q5)
lattices, showing that one otherwise arbitrary function in the
equilibria must be chosen to suppress instability.
@article{DellarDSFD04,
Author =
{Dellar, P. J.},
Title = {Non-hydrodynamic modes and general
equations of state in lattice {Boltzmann} equations},
Journal =
{Physica A},
Year = {2006},
Volume =
{362},
Pages = {132--138},
DOI = {doi:10.1016/j.physa.2005.09.012},
URL = {http://www.sciencedirect.com/science/article/B6TVG-4H7T8P5-1/2/95a56c63273881ad08c681119ce4791f}
}