1135 " /> 1135 " /> 1135 " />
 Chin. Phys. Lett.  2017, Vol. 34 Issue (2): 020502    DOI: 10.1088/0256-307X/34/2/020502
 GENERAL |
Note on Divergence of the Chapman–Enskog Expansion for Solving Boltzmann Equation
Nan-Xian Chen1**, Bo-Hua Sun2
1State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084
2Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town, South Africa
Nan-Xian Chen, Bo-Hua Sun 2017 Chin. Phys. Lett. 34 020502
 Download: PDF(346KB)   PDF(mobile)(347KB)   HTML Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
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 $\tau \geq 1$. 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.
Received: 16 January 2017      Published: 25 January 2017
 PACS: 05.20.Dd (Kinetic theory) 05.70.Ln (Nonequilibrium and irreversible thermodynamics) 02.30.Mv (Approximations and expansions)
Fund:

 TRENDMD: URL: http://cpl.iphy.ac.cn/10.1088/0256-307X/34/2/020502       OR      http://cpl.iphy.ac.cn/Y2017/V34/I2/020502