Kinetic boundary layers: on the adequate discretization of the Boltzmann collision operator

We develop criteria for the discretization of the Boltzmann collision operator under which linearized kinetic boundary layers exhibit the same algebraic structure as their continuous counterparts. These criteria are shown to be sufficient for the well-posedness of kinetic boundary layers. After the analysis of the discrete layer, an example illustrates how to include models which lead to differential algebraic problems. Existence and uniqueness of nonlinear boundary layers adjacent to an equilibrium state are proven.