Premium
A new consistent discrete‐velocity model for the Boltzmann equation
Author(s) -
Panferov Vladislav A.,
Heintz Alexei G.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.303
Subject(s) - boltzmann equation , mathematics , convergence (economics) , boltzmann constant , consistency (knowledge bases) , homogeneous , mathematical analysis , lattice boltzmann methods , space (punctuation) , collision , physics , geometry , mechanics , computer science , computer security , quantum mechanics , combinatorics , economics , thermodynamics , economic growth , operating system
Abstract This paper discusses the convergence of a new discrete‐velocity model to the Boltzmann equation. First the consistency of the collision integral approximation is proved. Based on this we prove the convergence of solutions for a modified model to renormalized solutions of the Boltzmann equation. In a numerical example, the solutions to the discrete problems are compared with the exact solution of the Boltzmann equation in the space‐homogeneous case. Copyright © 2002 John Wiley & Sons, Ltd.