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

作　　者：Nan-Xian Chen Bo-Hua Sun 陈难先;孙博华(State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University;Department of Mechanical Engineering, Cape Peninsula University of Technology)

机构地区：[1]State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University Beijing 100084 [2]Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town, South Africa

出　　处：《Chinese Physics Letters》2017年第2期15-17,共3页中国物理快报（英文版）

摘　　要：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≥ 1. Since then, this divergence problem has puzzled researchers for a century. Using a modified Mobius 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.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≥ 1. Since then, this divergence problem has puzzled researchers for a century. Using a modified Mobius 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.

分 类 号：O175[理学—数学]