Numerical approximation of Knudsen layer for the Euler-Poisson system

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In this work, we consider the computation of the boundary conditions for the linearized Euler-Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the boundary layers. In this paper, we will extend these techniques in the case of the coupled Euler-Poisson system.