A Mixed Spectral-Difference Method for the Steady State Boltzmann-Poisson System

The approximate solution of the Boltzmann transport equation via Galerkin-type series expansion methods leads to a system of conservation laws in space and time for the expansion coefficients. In this paper, we derive discretization methods for these equations in the mean field approximation, which are based on the entropy principles of the underlying Boltzmann equation, and discuss the performance of these discretizations and the series expansion approach in nonequilibrium regimes.

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