A computational study of residual kpp front speeds in time-periodic cellular flows in the small diffusion limit

Penghe Zu Long Chen Jack Xin

Fluid Dynamics and Shock Waves mathscidoc:1912.43878

Physica D: Nonlinear Phenomena, 311, 37-44, 2015.9
The minimal speeds (c) of the KolmogorovPetrovskyPiskunov (KPP) fronts at small diffusion ( 1) in a class of time-periodic cellular flows with chaotic streamlines is investigated in this paper. The variational principle of c reduces the computation to that of a principle eigenvalue problem on a periodic domain of a linear advectiondiffusion operator with spacetime periodic coefficients and small diffusion. To solve the advection dominated time-dependent eigenvalue problem efficiently over large time, a combination of spectral methods and finite element, as well as the associated fast solvers, are utilized to accelerate computation. In contrast to the scaling c= O ( 1/4) in steady cellular flows, a new relation c= O (1) as 1 is revealed in the time-periodic cellular flows due to the presence of chaotic streamlines. Residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub
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@inproceedings{penghe2015a,
  title={A computational study of residual kpp front speeds in time-periodic cellular flows in the small diffusion limit},
  author={Penghe Zu, Long Chen, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210403806517442},
  booktitle={Physica D: Nonlinear Phenomena},
  volume={311},
  pages={37-44},
  year={2015},
}
Penghe Zu, Long Chen, and Jack Xin. A computational study of residual kpp front speeds in time-periodic cellular flows in the small diffusion limit. 2015. Vol. 311. In Physica D: Nonlinear Phenomena. pp.37-44. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210403806517442.
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