A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources

@article{Filbet2010ACO,
  title={A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources},
  author={Francis Filbet and Shi Jin},
  journal={J. Comput. Physics},
  year={2010},
  volume={229},
  pages={7625-7648}
}
In this paper, we propose a general time discrete framework to design asymptotic preserving schemes for initial value problem of the Boltzmann kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free or relaxation time. We propose to penalize the nonlinear collision term by a BGK-type relaxation term, which can be solved explicitly even if discretized implicitly in time. Moreover, the BGK… CONTINUE READING

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