2013
DOI: 10.1142/s0129183113400160
|View full text |Cite
|
Sign up to set email alerts
|

Gauss Quadratures – The Keystone of Lattice Boltzmann Models

Abstract: In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB (N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss–Hermite quadrature. The second one is the SLB (N;K,L,M) family, derived by using the spherical coordinate system and the Gauss–Laguerre, as well as the Gauss–Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibr… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
9
0

Year Published

2015
2015
2020
2020

Publication Types

Select...
6
1

Relationship

3
4

Authors

Journals

citations
Cited by 14 publications
(9 citation statements)
references
References 31 publications
0
9
0
Order By: Relevance
“…In the D-dimensional LB model where the full-range Gauss-Hermite quadrature of order Q is used on each Cartesian axis, we have 1 ≤ k α ≤ Q for all α, 1 ≤ α ≤ D, and hence the momentum set {p κ } has K = Q D elements. The order Q of the quadrature should satisfy the condition Q ≥ N +1 in order to retrieve all the moments of f (x, p, t) up to order N [11,34,35,37]. Although the number K of the quadrature points can be reduced by very elaborated pruning techniques by sacrificing some higher order moments of the distribution function [11,38,39], we will not consider such models in this paper.…”
Section: Discretization Of the Momentum Space Evolution Equations Anmentioning
confidence: 99%
“…In the D-dimensional LB model where the full-range Gauss-Hermite quadrature of order Q is used on each Cartesian axis, we have 1 ≤ k α ≤ Q for all α, 1 ≤ α ≤ D, and hence the momentum set {p κ } has K = Q D elements. The order Q of the quadrature should satisfy the condition Q ≥ N +1 in order to retrieve all the moments of f (x, p, t) up to order N [11,34,35,37]. Although the number K of the quadrature points can be reduced by very elaborated pruning techniques by sacrificing some higher order moments of the distribution function [11,38,39], we will not consider such models in this paper.…”
Section: Discretization Of the Momentum Space Evolution Equations Anmentioning
confidence: 99%
“…The minimum number of the velocity vectors in the two-dimensional (D = 2) isothermal LB model based on the full-range Gauss-Hermite quadrature ensuring all the moments of f (x, v, t) up to order N = 2 is K = (N + 1) D = 9. 4, 15,16,17 As usual in the current LB models involving the BGK collision term, 4 the nondimensionalized form of the evolution equation of the functions f k ≡ f (x, v k , t) for the force-free flow of a single-component fluid is…”
Section: Lattice Boltzmann Modelsmentioning
confidence: 99%
“…. ξ α N dξ, are thereafter recovered using appropriate quadrature methods in the velocity space [25,[43][44][45][46].…”
Section: Description Of the Modelmentioning
confidence: 99%