A numerical scheme for the quantum Boltzmann equation with stiff collision terms
Francis Filbet, Jingwei Hu, Shi Jin (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision terms. A class of asymptotic-preserving schemes was introduced in [F. Filbet and S. Jin,J. Comput. Phys. 229 (2010) 7625–7648] to handle this kind of problems. The idea is to penalize the stiff collision term by a BGK type operator. This method, however, encounters its own difficulty when applied to the quantum Boltzmann equation. To define the quantum...