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Front quenching in the G-equation model induced by straining of cellular flow

Jack Xin Yifeng Yu

Fluid Dynamics and Shock Waves mathscidoc:1912.43889

Archive for Rational Mechanics and Analysis, 214, (1), 1-34, 2014.10
We study homogenization of the G-equation with a flow straining term (or the strain G-equation) in two dimensional periodic cellular flow. The strain G-equation is a highly non-coercive and non-convex level set HamiltonJacobi equation. The main objective is to investigate how the flow induced straining (the nonconvex term) influences front propagation as the flow intensity <i>A</i> increases. Three distinct regimes are identified. When <i>A</i> is below the critical level, homogenization holds and the turbulent flame speed <i>s</i> <sub>T</sub> (effective Hamiltonian) is well-defined for any periodic flow with small divergence and is enhanced by the cellular flow as <i>s</i> <sub>T</sub> <i>O</i>(<i>A</i>/log <i>A</i>). In the second regime where <i>A</i> is slightly above the critical value, homogenization breaks down, and <i>s</i> <sub>T</sub> is not well-defined along any direction. Solutions become a mixture of a fast moving part and a stagnant part. When <i>A</i> is
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@inproceedings{jack2014front,
  title={Front quenching in the G-equation model induced by straining of cellular flow},
  author={Jack Xin, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210450724693453},
  booktitle={Archive for Rational Mechanics and Analysis},
  volume={214},
  number={1},
  pages={1-34},
  year={2014},
}
Jack Xin, and Yifeng Yu. Front quenching in the G-equation model induced by straining of cellular flow. 2014. Vol. 214. In Archive for Rational Mechanics and Analysis. pp.1-34. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210450724693453.
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