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Volume 8, Issue 1
Model Reduction of a Two-Dimensional Kinetic Swarming Model by Operator Projections

Junming Duan, Yangyu Kuang & Huazhong Tang

DOI: 10.4208/eajam.170617.141117a

East Asian J. Appl. Math., 8 (2018), pp. 151-180.

Published online: 2018-02

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  • Abstract

Hyperbolic, rotation invariant moment systems are derived for a non-linear kinetic description of two-dimensional Vicsek swarming model. The systems also preserve mass conservation, and numerical experiments show that this approach captures the key features of the model such as shock waves, contact discontinuities, rarefaction waves, vortex formations. If the system order increases, the solutions of the moment systems converge to the solution of the corresponding kinetic equation.

  • Keywords

Moment method, hyperbolicity, kinetic equation, model reduction, projection operator.

  • AMS Subject Headings

82C40, 35L60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-151, author = {Junming Duan, Yangyu Kuang and Huazhong Tang}, title = {Model Reduction of a Two-Dimensional Kinetic Swarming Model by Operator Projections}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {1}, pages = {151--180}, abstract = {

Hyperbolic, rotation invariant moment systems are derived for a non-linear kinetic description of two-dimensional Vicsek swarming model. The systems also preserve mass conservation, and numerical experiments show that this approach captures the key features of the model such as shock waves, contact discontinuities, rarefaction waves, vortex formations. If the system order increases, the solutions of the moment systems converge to the solution of the corresponding kinetic equation.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.170617.141117a}, url = {http://global-sci.org/intro/article_detail/eajam/10890.html} }
TY - JOUR T1 - Model Reduction of a Two-Dimensional Kinetic Swarming Model by Operator Projections AU - Junming Duan, Yangyu Kuang & Huazhong Tang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 151 EP - 180 PY - 2018 DA - 2018/02 SN - 8 DO - http://doi.org/10.4208/eajam.170617.141117a UR - https://global-sci.org/intro/article_detail/eajam/10890.html KW - Moment method, hyperbolicity, kinetic equation, model reduction, projection operator. AB -

Hyperbolic, rotation invariant moment systems are derived for a non-linear kinetic description of two-dimensional Vicsek swarming model. The systems also preserve mass conservation, and numerical experiments show that this approach captures the key features of the model such as shock waves, contact discontinuities, rarefaction waves, vortex formations. If the system order increases, the solutions of the moment systems converge to the solution of the corresponding kinetic equation.

Junming Duan, Yangyu Kuang and Huazhong Tang. (2018). Model Reduction of a Two-Dimensional Kinetic Swarming Model by Operator Projections. East Asian Journal on Applied Mathematics. 8 (1). 151-180. doi:10.4208/eajam.170617.141117a
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