Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

Yu-Yu Liu Jack Xin Yifeng Yu

Analysis of PDEs mathscidoc:1912.43869

Archive for rational mechanics and analysis, 202, (2), 461-492, 2011.11
G-equations are well-known front propagation models in turbulent combustion which describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are HamiltonJacobi equations with convex (<i>L</i> <sup>1</sup> type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $${\bar H}$$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed <i>s</i> <sub>T</sub>. An important problem in turbulent combustion theory is to study properties of <i>s</i> <sub>T</sub>, in particular how <i>s</i> <sub>T</sub> depends on the flow amplitude <i>A</i>. In this paper, we study the behavior of $${\bar H=\bar H(A,d)}$$ as <i>A</i> + at any fixed diffusion constant <i>d</i> &gt; 0. For cellular flow, we show that$$\bar H(A,d)\leqq
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@inproceedings{yu-yu2011asymptotics,
  title={Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows},
  author={Yu-Yu Liu, Jack Xin, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210326877351433},
  booktitle={Archive for rational mechanics and analysis},
  volume={202},
  number={2},
  pages={461-492},
  year={2011},
}
Yu-Yu Liu, Jack Xin, and Yifeng Yu. Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows. 2011. Vol. 202. In Archive for rational mechanics and analysis. pp.461-492. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210326877351433.
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