Analysis of the parametric models of passive scalar transport used in the lattice Boltzmann method

Research output

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 languageEnglish
JournalComputers and Mathematics with Applications
DOIs
Publication statusE-pub ahead of print - 21 Sep 2019

Fingerprint

Passive Scalar
Lattice Boltzmann Method
Parametric Model
Stability Analysis
Numerical Dispersion
Runge-Kutta
Advection
Finite Difference Scheme
Stability Condition
Test Problems
Initial conditions
Model
Higher Order

Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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title = "Analysis of the parametric models of passive scalar transport used in the lattice Boltzmann method",
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.",
keywords = "Lattice Boltzmann method, Numerical diffusion, Numerical dispersion, Passive scalar transport, Runge–Kutta methods, Stability",
author = "Krivovichev, {Gerasim V.}",
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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.

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