Abstract
The paper is devoted to the analysis of passive scalar transport models, used in the lattice Boltzmann method. The case of the pure advection process, without physical diffusion, is considered. The models, proposed by other authors, the modifications of these models and new high-order finite-difference schemes, based on the extended Runge–Kutta-like formulae, are analyzed. The attention is focused on the stability analysis, analysis of the fictitious numerical effects and on the investigation of the sensitivity of accuracy order to the parameter values. The stability analysis is based on the von Neumann method. The influence of the parameter values on the stability is demonstrated. Stability conditions are obtained. Numerical dispersion and diffusion are analyzed. Test problems with discontinuous and smooth initial conditions are considered. The sensitivity of the accuracy order on the parameter values is analyzed.
| Original language | English |
|---|---|
| Journal | Computers and Mathematics with Applications |
| DOIs | |
| Publication status | E-pub ahead of print - 21 Sep 2019 |
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Scopus subject areas
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics
Cite this
}
TY - JOUR
T1 - Analysis of the parametric models of passive scalar transport used in the lattice Boltzmann method
AU - Krivovichev, Gerasim V.
PY - 2019/9/21
Y1 - 2019/9/21
N2 - The paper is devoted to the analysis of passive scalar transport models, used in the lattice Boltzmann method. The case of the pure advection process, without physical diffusion, is considered. The models, proposed by other authors, the modifications of these models and new high-order finite-difference schemes, based on the extended Runge–Kutta-like formulae, are analyzed. The attention is focused on the stability analysis, analysis of the fictitious numerical effects and on the investigation of the sensitivity of accuracy order to the parameter values. The stability analysis is based on the von Neumann method. The influence of the parameter values on the stability is demonstrated. Stability conditions are obtained. Numerical dispersion and diffusion are analyzed. Test problems with discontinuous and smooth initial conditions are considered. The sensitivity of the accuracy order on the parameter values is analyzed.
AB - The paper is devoted to the analysis of passive scalar transport models, used in the lattice Boltzmann method. The case of the pure advection process, without physical diffusion, is considered. The models, proposed by other authors, the modifications of these models and new high-order finite-difference schemes, based on the extended Runge–Kutta-like formulae, are analyzed. The attention is focused on the stability analysis, analysis of the fictitious numerical effects and on the investigation of the sensitivity of accuracy order to the parameter values. The stability analysis is based on the von Neumann method. The influence of the parameter values on the stability is demonstrated. Stability conditions are obtained. Numerical dispersion and diffusion are analyzed. Test problems with discontinuous and smooth initial conditions are considered. The sensitivity of the accuracy order on the parameter values is analyzed.
KW - Lattice Boltzmann method
KW - Numerical diffusion
KW - Numerical dispersion
KW - Passive scalar transport
KW - Runge–Kutta methods
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=85072334080&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2019.09.010
DO - 10.1016/j.camwa.2019.09.010
M3 - Article
AN - SCOPUS:85072334080
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
ER -