Comparison of analysis techniques for the lattice Boltzmann method

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• 作者：Alfonso Caiazzo ; Michael Junk ; Martin Rheinlä ; nder
• 关键词：Chapman– ; Enskog expansion ; Lattice Boltzmann equation ; Super-Burnett equation
• 刊名：Computers and Mathematics with Applications
• 出版年：2009
• 出版时间：September 2009
• 年：2009
• 卷：58
• 期：5
• 页码：883-897
• 全文大小：771 K

文摘

We show that the Chapman–Enskog expansion can be viewed as a special instance of a general expansion procedure which also encompasses other methods like the regular error expansion and multi-scale techniques and that any two expansions which properly describe the lattice Boltzmann solution necessarily coincide up to higher order terms. For a model problem, both the regular error expansion and the Chapman–Enskog expansion are carried out. It turns out that the classical Chapman–Enskog method leads to an unstable equation at super-Burnett order in a parameter regime for which the underlying lattice Boltzmann algorithm is stable. However, our approach naturally allows us to consider variants of the super-Burnett equation which do not suffer from instabilities. The article concludes with a detailed comparison of the Chapman–Enskog and the regular error expansion.