On rotational invariance of lattice Boltzmann schemes

被引：17

作者：

Augier, Adeline ^{[1
]}

Dubois, Francois ^{[1
,2
,3
]}

Graille, Benjamin ^{[1
]}

Lallemand, Pierre ^{[4
,5
]}

机构：

[1] Univ Paris 11, Dept Math, F-91405 Orsay, France

[2] Dept Math, Paris, France

[3] LMSSC, Paris, France

[4] CNRS, Paris, France

[5] Beijing Sci Comp Res Ctr, Beijing, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 67卷 / 02期

关键词：

Acoustics; Taylor expansion method; Linearized Navier-Stokes; Isotropy; NAVIER-STOKES EQUATION; ISOTROPY; MODELS;

D O I：

10.1016/j.camwa.2013.06.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose the derivation of acoustic-type isotropic partial differential equations that are equivalent to linear lattice Boltzmann schemes with a density scalar field and a momentum vector field as conserved moments. The corresponding linear equivalent partial differential equations are generated with a new "Berliner version" of the Taylor expansion method. The details of the implementation are presented. These ideas are applied for the D2Q9, D2Q13, D3Q19 and D3Q27 lattice Boltzmann schemes. Some limitations associated with necessary stability conditions are also presented. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：239 / 255

页数：17

共 23 条

[1]

[Anonymous], 1998, Representations and Invariants of the Classical Groups

[2]

Augier Adeline, 2012, ESAIM Proceedings, V35, P191, DOI 10.1051/proc/201235013

[3] Linear lattice Boltzmann schemes for acoustic: Parameter choices and isotropy properties [J].

Augier, Adeline ;

Dubois, Francois ;

Gouarin, Loic ;

Graille, Benjamin .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 65 (06) :845-863

[4] Moment isotropy and discrete rotational symmetry of two-dimensional lattice vectors [J].

Chen, Hudong ;

Orszag, Steven .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2011, 369 (1944) :2176-2183

[5]

d'Humieres D., 1992, AIAA PROGR ASTRONAUT, V159, P450

[6]

Dubois F., 2011, METHODE GEN CA UNPUB

[7]

Dubois F., PEDAGOGICAL EX UNPUB

[8] Equivalent partial differential equations of a lattice Boltzmann scheme [J].

Dubois, Francois .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 55 (07) :1441-1449

[9] Stable lattice Boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves [J].

Dubois, Francois .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 65 (02) :142-159

[10] Quartic parameters for acoustic applications of lattice Boltzmann scheme [J].

Dubois, Francois ;

Lallemand, Pierre .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (12) :3404-3416

← 1 2 3 →