Title
Numerical extraction of a macroscopic PDE and a lifting operator from a lattice Boltzmann model Numerical extraction of a macroscopic PDE and a lifting operator from a lattice Boltzmann model
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Physics
Source (journal)
Multiscale modeling and simulation
Volume/pages
10(2012) :3 , p. 766-791
ISI
000311628100005
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Lifting operators play an important role in starting a lattice Boltzmann model from a given initial density. The density, a macroscopic variable, needs to be mapped to the distribution functions, mesoscopic variables, of the lattice Boltzmann model. Several methods proposed as lifting operators have been tested and discussed in the literature. The most famous methods are an analytically found lifting operator, like the Chapman--Enskog expansion, and a numerical method, like the Constrained Runs algorithm, to arrive at an implicit expression for the unknown distribution functions with the help of the density. This paper proposes a lifting operator that alleviates several drawbacks of these existing methods. In particular, we focus on the computational expense and the analytical work that needs to be done. The proposed lifting operator, a numerical Chapman--Enskog expansion, obtains the coefficients of the Chapman--Enskog expansion numerically. Another important feature of the use of lifting operators is found in hybrid models. There the lattice Boltzmann model is spatially coupled with a model based on a more macroscopic description, for example an advection-diffusion-reaction equation. In one part of the domain, the lattice Boltzmann model is used, while in another part, the more macroscopic model is used. Such a hybrid coupling results in missing data at the interfaces between the different models. A lifting operator is then an important tool since the lattice Boltzmann model is typically described by more variables than a model based on a macroscopic partial differential equation.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/078cdd/588479c4.pdf
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