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arXiv · 1808.10739

Note on Divergence of the Chapman-Enskog Expansion for Solving Boltzmann Equation

Nanxian Chen·Bohua Sun
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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 $τ\geq 1$. Even since this divergence problem has puzzled this subject for a century. By using a modified Möbius series inversion formula, this paper proposes 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 provide the best-so-far explanation on some unbelievable scenarios occurred in previous practice.

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Nanxian Chen, Bohua Sun. 2018-07-30. Note on Divergence of the Chapman-Enskog Expansion for Solving Boltzmann Equation. https://doi.org/10.1088/0256-307x%2F34%2F2%2F020502

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