Factorization symmetry in the lattice Boltzmann method
Factorization symmetry in the lattice Boltzmann method
A non-perturbative algebraic theory of the lattice Boltzmann method is developed based on the symmetry of a product.
It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which imposes restricted extension of higher-order Gaussian moments, (ii) A special quasi-equilibrium distribution function found analytically in closed form on the product-lattice in two and three spatial dimensions, and which proves the factorization of quasi-equilibrium moments, and (iii) An algebraic method of pruning based on a one-into-one relation between groups of discrete velocities and moments. Two routes of constructing lattice Boltzmann equilibria are distinguished. The present theory includes previously known limiting and special cases
of lattices, and enables automated derivation of lattice Boltzmann models from two-dimensional tables, by finding the roots of one polynomial and solving a few linear systems
kinetic theory, lattice boltzmann method
1530-1548
Karlin, I. V.
82f739e9-de61-47ab-b714-60fac58d1779
Asinari, P.
9db3ca0d-3a5f-40b7-94a6-f11928f74b3d
15 April 2010
Karlin, I. V.
82f739e9-de61-47ab-b714-60fac58d1779
Asinari, P.
9db3ca0d-3a5f-40b7-94a6-f11928f74b3d
Karlin, I. V. and Asinari, P.
(2010)
Factorization symmetry in the lattice Boltzmann method.
Physica A: Statistical Mechanics and its Applications, 389 (8), .
(doi:10.1016/j.physa.2009.12.032).
Abstract
A non-perturbative algebraic theory of the lattice Boltzmann method is developed based on the symmetry of a product.
It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which imposes restricted extension of higher-order Gaussian moments, (ii) A special quasi-equilibrium distribution function found analytically in closed form on the product-lattice in two and three spatial dimensions, and which proves the factorization of quasi-equilibrium moments, and (iii) An algebraic method of pruning based on a one-into-one relation between groups of discrete velocities and moments. Two routes of constructing lattice Boltzmann equilibria are distinguished. The present theory includes previously known limiting and special cases
of lattices, and enables automated derivation of lattice Boltzmann models from two-dimensional tables, by finding the roots of one polynomial and solving a few linear systems
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Published date: 15 April 2010
Keywords:
kinetic theory, lattice boltzmann method
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Local EPrints ID: 155869
URI: http://eprints.soton.ac.uk/id/eprint/155869
ISSN: 0378-4371
PURE UUID: 8f94a104-4861-4fac-905f-75c71c34441d
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Date deposited: 28 May 2010 15:53
Last modified: 14 Mar 2024 01:41
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Author:
I. V. Karlin
Author:
P. Asinari
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