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Model Reduction of Kinetic Equations by Operator Projection

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Abstract

By a further study of the mechanism of the hyperbolic regularization of the moment system for the Boltzmann equation proposed in Cai et al. (Commun Math Sci 11(2):547–571, 2013), we point out that the key point is treating the time and space derivative in the same way. Based on this understanding, a uniform framework to derive globally hyperbolic moment systems from kinetic equations using an operator projection method is proposed. The framework is so concise and clear that it can be treated as an algorithm with four inputs to derive hyperbolic moment systems by routine calculations. Almost all existing globally hyperbolic moment systems can be included in the framework, as well as some new moment systems including globally hyperbolic regularized versions of Grad’s ordered moment systems and a multi-dimensional extension of the quadrature-based moment system.

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Notes

  1. See discussion on the admissible subspace for any moment method in Ref. [14].

  2. \(\varvec{\eta }_1\) can be treated as a set, but uniqueness demands that every element of \(\varvec{\eta }_1\) cannot be expressed by the others. For example, \(\{\rho , \theta ,p\}\) is not allowed because \(p=\rho \theta \), while \(\{\rho ,u,\theta \}\) is allowed.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, China

    Yuwei Fan & Jun Li

  2. Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany

    Julian Koellermeier & Manuel Torrilhon

  3. CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing, China

    Ruo Li

Authors
  1. Yuwei Fan
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  2. Julian Koellermeier
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  3. Jun Li
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  4. Ruo Li
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  5. Manuel Torrilhon
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Correspondence to Yuwei Fan.

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Fan, Y., Koellermeier, J., Li, J. et al. Model Reduction of Kinetic Equations by Operator Projection. J Stat Phys 162, 457–486 (2016). https://doi.org/10.1007/s10955-015-1384-9

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  • DOI: https://doi.org/10.1007/s10955-015-1384-9

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