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Convergence of a discrete-velocity model for the Boltzmann-BGK equation

✍ Scribed by L Mieussens

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
825 KB
Volume
41
Category
Article
ISSN
0898-1221

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✦ Synopsis

We prove the convergence of a conservative and entropic discrete-velocity model for the Bathnagar-Gross-Krook (BGK) equation. In this model, the approximation of the Maxwellian is based on a discrete entropy minimization principle. The main difficulty, due to its implicit definition, is to prove that this approximation is consistent. We also demonstrate the existence and uniqueness of a solution to the discrete-velocity model, by using a fixed-point theorem. Finally, the model is written in a continuous equation form, and we prove the convergence of its solution toward a solution of the BGK equation.

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