Diffusion approximations of a linear kinetic equation with inelastic scattering: Asymptotic analysis and numerical results

Abstract

In this work we consider the diffusion approximation of the Boltzmann equation in the Lorentz gas limit with inelastic scattering kernel and in the absence of fields. We derive the diffusion approximation by using the compressed Chapman-Enskog method and we evaluate numerically the error of the diffusion approximation for several values of the collision frequency and several initial conditions. We also present numerical results showing the relevant aspects of the time evolution of the distribution function in this physical setting.

Key Words:

• kinetic theory
• inelastic scattering
• Lorentz gas
• diffusion approximation.