Characteristic-based finite-difference schemes for the simulation of convection–diffusion equation by the finite-difference-based lattice Boltzmann methods

Standard

Characteristic-based finite-difference schemes for the simulation of convection–diffusion equation by the finite-difference-based lattice Boltzmann methods. / Krivovichev, G. V.

в: International Journal of Computer Mathematics, Том 98, № 10, 18.01.2021, стр. 1991-2007.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{4ca3795e16e54398872428380eca0c8b,

title = "Characteristic-based finite-difference schemes for the simulation of convection–diffusion equation by the finite-difference-based lattice Boltzmann methods",

abstract = "The paper is devoted to the analysis of characteristic-based (CB) schemes for the simulation of the convection–diffusion equation by the lattice Boltzmann method (LBM). Numerical schemes from the first order to fourth one are considered. The stability analysis is realized by the von Neumann method. The stability domains of the schemes are constructed. It is demonstrated that the areas of the stability domains for CB schemes are larger than the domains for the schemes, constructed by the traditional approach, based on the discretization at the Cartesian axes directions. By the solution of the numerical examples with the smooth initial conditions, it is demonstrated that the practical convergence rates of the schemes are consistent with the theoretical values. As it is shown, the proposed schemes can be used for the cases of the Peclet number values, when the classical LBM is unstable.",

keywords = "convection, diffusion, finite-difference schemes, Lattice Boltzmann method, stability, MODELS",

author = "Krivovichev, {G. V.}",

note = "Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2021",

month = jan,

day = "18",

doi = "10.1080/00207160.2020.1870680",

language = "English",

volume = "98",

pages = "1991--2007",

journal = "International Journal of Computer Mathematics",

issn = "0020-7160",

publisher = "Taylor & Francis",

number = "10",

}

RIS

TY - JOUR

T1 - Characteristic-based finite-difference schemes for the simulation of convection–diffusion equation by the finite-difference-based lattice Boltzmann methods

AU - Krivovichev, G. V.

PY - 2021/1/18

Y1 - 2021/1/18

N2 - The paper is devoted to the analysis of characteristic-based (CB) schemes for the simulation of the convection–diffusion equation by the lattice Boltzmann method (LBM). Numerical schemes from the first order to fourth one are considered. The stability analysis is realized by the von Neumann method. The stability domains of the schemes are constructed. It is demonstrated that the areas of the stability domains for CB schemes are larger than the domains for the schemes, constructed by the traditional approach, based on the discretization at the Cartesian axes directions. By the solution of the numerical examples with the smooth initial conditions, it is demonstrated that the practical convergence rates of the schemes are consistent with the theoretical values. As it is shown, the proposed schemes can be used for the cases of the Peclet number values, when the classical LBM is unstable.

AB - The paper is devoted to the analysis of characteristic-based (CB) schemes for the simulation of the convection–diffusion equation by the lattice Boltzmann method (LBM). Numerical schemes from the first order to fourth one are considered. The stability analysis is realized by the von Neumann method. The stability domains of the schemes are constructed. It is demonstrated that the areas of the stability domains for CB schemes are larger than the domains for the schemes, constructed by the traditional approach, based on the discretization at the Cartesian axes directions. By the solution of the numerical examples with the smooth initial conditions, it is demonstrated that the practical convergence rates of the schemes are consistent with the theoretical values. As it is shown, the proposed schemes can be used for the cases of the Peclet number values, when the classical LBM is unstable.

KW - convection

KW - diffusion

KW - finite-difference schemes

KW - Lattice Boltzmann method

KW - stability

KW - MODELS

UR - http://www.scopus.com/inward/record.url?scp=85099570854&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/66ca8bdb-63cb-3cd3-aff2-94cc91c70016/

U2 - 10.1080/00207160.2020.1870680

DO - 10.1080/00207160.2020.1870680

M3 - Article

AN - SCOPUS:85099570854

VL - 98

SP - 1991

EP - 2007

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 10

ER -

ID: 73720979