%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 }