Anisotropic scattering kernel: Generalized and modified Maxwell boundary conditions

Abstract

This article presents a model of a scattering kernel of boundary conditions for the Boltzmann equation. The proposed scattering kernel is based on an anisotropic accommodation argument. Three parameters equal to the momentum accommodation coefficients are shown as characterizing the influence of each direction. First the new scattering kernel is derived from a phenomenological criticism of the first form of the scattering kernel proposed by Maxwell; then the same result is established from an analytic approach based on the spectral nature of the linear integral operator associated to the scattering kernel problem. As a result, the model provides a correct form of scattering kernel to handle the influence of each direction in particle collisions with the wall. Finally independent accommodation of each internal mode is added to extend the model to the case of polyatomic gases.