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

【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 M?bius 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.更多还原

【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≥1. Since then, this divergence problem has puzzled researchers for a century. Using a modified M?bius 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.更多还原