  Based on the Hermite expansion of the distribution function, we introduce a
Galerkin spectral method for the spatially homogeneous Boltzmann equation with
the realistic inverse-power-law models. A practical algorithm is proposed to
evaluate the coefficients in the spectral method with high accuracy, and these
coefficients are also used to construct new computationally affordable
collision models. Numerical experiments show that our method captures the
low-order moments very efficiently.
