Novel Trends in Lattice-Boltzmann Methods

Book Series: Progress in Computational Physics (PiCP)

Volume 3


Matthias Ehrhardt

DOI: 10.2174/97816080571601130301
eISBN: 978-1-60805-716-0, 2013
ISBN: 978-1-60805-717-7
ISSN: 2589-3017 (Print)
ISSN: 1879-4661 (Online)

Indexed in: EBSCO, Ulrich's Periodicals Directory.

Progress in Computational Physics is an e-book series devoted to recent research trends in computational physics. It contains chapters...[view complete introduction]
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An Introduction to the Lattice Boltzmann Method for Coupled Problems

- Pp. 3-30 (28)

Daniel Heubes, Andreas Bartel and Matthias Ehrhardt


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. </p><p> 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.

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