Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows

Yu-Yu Liu Jack Xin Yifeng Yu

Analysis of PDEs mathscidoc:1912.43916

Mathematical Modelling of Natural Phenomena, 8, (3), 198-205, 2013
We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The curvature-strain G-equations are also non-convex with degenerate diffusion. The computation is based on monotone finite difference discretization and weighted essentially nonoscillatory (WENO) methods. We found that the large time front speeds lock into the frequency of time periodic cellular flows in curvature-strain G-equations similar to what occurs in the basic inviscid G-equation. However, such frequency locking phenomenon disappears in viscous G-equation, and in the inviscid G-equation if time periodic oscillation of the cellular flow is replaced by time stochastic oscillation.
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@inproceedings{yu-yu2013turbulent,
  title={Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows},
  author={Yu-Yu Liu, Jack Xin, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210628790823480},
  booktitle={Mathematical Modelling of Natural Phenomena},
  volume={8},
  number={3},
  pages={198-205},
  year={2013},
}
Yu-Yu Liu, Jack Xin, and Yifeng Yu. Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows. 2013. Vol. 8. In Mathematical Modelling of Natural Phenomena. pp.198-205. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210628790823480.
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