On the Convergence of the Solution to the Gross-Jackson's Kinetic Model Equation

Abstract

The Boltzmann equation with the Gross-Jackson's collision model, i.e., the Gross-Jackson's model equation was solved by applying the half-range Hermite polynomials. It was found that the solution to the model equation converged rather rapidly as long as the scaling factor β was of 0(1). The rate of the convergence seemed to be dependent on the value of β but if the collision term included sufficient eigen-values to the Boltzmann collision operator, the solution was, in practice, independent of the value of β. The velocity slip coefficient obtained showed a good agreement with the result of the direct Monte Carlo simulation to the full Boltzmann equation.