The first part of this introduction is devoted to the known derivation of the lattice Boltzmann method (LBM): We track two different derivations, a historical one (via lattice gas automata) and a theoretical version (via a discretization of the Boltzmann equation). Thereby the collision term is approximated with a single relaxation time model (BGK) and we motivate the introduction of this common approximation. By applying a multiscale expansion (Chapman-Enskog), the solution of the numerical method is verified as a meaningful approximation of the solution of the Navier-Stokes equations. To state a well posed problem, common boundary conditions are introduced and their realization within a LBM is discussed.
In the second part, the LBM is extended to handle coupled problems. Four cases are investigated: (i) multiphase and multicomponent flow, (ii) additional forces, (iii) the coupling to heat transport, (iv) coupling of electric circuits with power dissipation (as heat) and heat transport.
%0 Book Section
%1 heubes2013introduction
%A Heubes, Daniel
%A Bartel, Andreas
%A Ehrhardt, Matthias
%B Novel Trends in Lattice-Boltzmann Methods
%D 2013
%I Bentham Science
%K 76m28-particle-methods-and-lattice-gas-methods-in-fluid-mechanics
%P 3-30
%R 10.2174/9781608057160113030004
%T An Introduction to the Lattice Boltzmann Method for Coupled Problems
%U http://www.eurekaselect.com/chapter/5242
%V 3
%X The first part of this introduction is devoted to the known derivation of the lattice Boltzmann method (LBM): We track two different derivations, a historical one (via lattice gas automata) and a theoretical version (via a discretization of the Boltzmann equation). Thereby the collision term is approximated with a single relaxation time model (BGK) and we motivate the introduction of this common approximation. By applying a multiscale expansion (Chapman-Enskog), the solution of the numerical method is verified as a meaningful approximation of the solution of the Navier-Stokes equations. To state a well posed problem, common boundary conditions are introduced and their realization within a LBM is discussed.
In the second part, the LBM is extended to handle coupled problems. Four cases are investigated: (i) multiphase and multicomponent flow, (ii) additional forces, (iii) the coupling to heat transport, (iv) coupling of electric circuits with power dissipation (as heat) and heat transport.
@incollection{heubes2013introduction,
abstract = {The first part of this introduction is devoted to the known derivation of the lattice Boltzmann method (LBM): We track two different derivations, a historical one (via lattice gas automata) and a theoretical version (via a discretization of the Boltzmann equation). Thereby the collision term is approximated with a single relaxation time model (BGK) and we motivate the introduction of this common approximation. By applying a multiscale expansion (Chapman-Enskog), the solution of the numerical method is verified as a meaningful approximation of the solution of the Navier-Stokes equations. To state a well posed problem, common boundary conditions are introduced and their realization within a LBM is discussed.
In the second part, the LBM is extended to handle coupled problems. Four cases are investigated: (i) multiphase and multicomponent flow, (ii) additional forces, (iii) the coupling to heat transport, (iv) coupling of electric circuits with power dissipation (as heat) and heat transport.},
added-at = {2023-05-16T08:40:03.000+0200},
author = {Heubes, Daniel and Bartel, Andreas and Ehrhardt, Matthias},
biburl = {https://www.bibsonomy.org/bibtex/2384aea2e4a6abb8f8969900659231ce2/gdmcbain},
booktitle = {Novel Trends in Lattice-Boltzmann Methods},
doi = {10.2174/9781608057160113030004},
interhash = {0210a199cad667d34fed9120635b9bc8},
intrahash = {384aea2e4a6abb8f8969900659231ce2},
keywords = {76m28-particle-methods-and-lattice-gas-methods-in-fluid-mechanics},
pages = {3-30},
publisher = {Bentham Science},
series = {Progress in Computational Physics},
timestamp = {2023-05-16T08:40:03.000+0200},
title = {An Introduction to the Lattice Boltzmann Method for Coupled Problems},
url = {http://www.eurekaselect.com/chapter/5242},
volume = 3,
year = 2013
}