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Erschienen in:
2011 | OriginalPaper | Buchkapitel
A Numerical Analyst’s View of the Lattice Boltzmann Method
verfasst von : Jeremy Levesley, Alexander N. Gorban, David Packwood
Erschienen in: Approximation Algorithms for Complex Systems
Verlag: Springer Berlin Heidelberg
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The purpose of this paper is to raise the profile of the Lattice Boltzmann method (LBM) as a computational method for solving fluid flow problems. We put forward the point of view that the method need not be seen as a discretisation of the Boltzmann equation, and also propose an alternative route from microscopic to macroscopic dynamics, traditionally taken via the Chapman-Enskog procedure. In that process the microscopic description is decomposed into processes at different time scales, parametrised with the Knudsen number. In our exposition we use the time step as a parameter for expanding the solution. This makes the treatment here more amenable to numerical analysts. We explain a method by which one may ameliorate the inevitable instabilities arising when trying to solve a convection- dominated problem, entropic filtering.