Sonine Polynomial Solution of the Boltzmann Equation for Relaxation of Initially Nonequilibrium Distribution

Using the Sonine polynomial expansion method the nonlinear Boltzmann equation for time-dependent spatially uniform gases is solved to examine the relaxation of an initially nonequilibrium distribution toward the equilibrium. For an inverse-fifth power law force, a simple analytical expression is presented for equations for expansion coefficients. As a result the higher-order expansion coefficients as well as the lower-order ones are obtained, so that the decay of larger initial departure of the distribution function from the equilibrium is dealt with. The resulting distribution function is compared with the corresponding one obtained on the basis of the Bhatnagar-Gross-Krook model. The latter model is shown to be adequate only when the departure of distribution function from the equilibrium becomes small.