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Title: Note on divergence of the Chapman–Enskog expansion for solving boltzmann equation
Authors: Chen, Nan-Xian 
Sun, BoHua 
Keywords: Divergence;Chapman–Enskog expansion;Boltzmann equation;Möbius series inversion formula
Issue Date: 2017
Publisher: Chinese Physics Letters
Source: Nan-Xian Chen and Bo-Hua Sun 2017 Chinese Phys. Lett. 34 020502
Abstract: Within about a year (1916–1917) Chapman and Enskog independently proposed an important expansion for solving the Boltzmann equation. However, the expansion is divergent or indeterminant in the case of relaxation time $\tau \geqslant 1$. Since then, this divergence problem has puzzled researchers for a century. Using a modified Möbius series inversion formula, we propose a modified Chapman–Enskog expansion with a variable upper limit of the summation. The new expansion can give not only a convergent summation but also the best-so-far explanation on some unbelievable scenarios occurring in previous practice.
ISSN: 0256-307X
Appears in Collections:Eng - Journal articles (DHET subsidised)

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