Title 



Numerical extraction of a macroscopic PDE and a lifting operator from a lattice Boltzmann model
 
Author 



 
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 ChapmanEnskog 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 ChapmanEnskog expansion, obtains the coefficients of the ChapmanEnskog 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 advectiondiffusionreaction 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.   
Language 



English
 
Source (journal) 



Multiscale modeling and simulation  
Publication 



2012
 
Volume/pages 



10:3(2012), p. 766791
 
ISI 



000311628100005
 
Full text (Publisher's DOI) 


  
Full text (open access) 


  
