A numerical study of turbulent flame speeds of curvature and strain G-equations in cellular flows

Yu-Yu Liu Jack Xin Yifeng Yu

Numerical Analysis and Scientific Computing mathscidoc:1912.43890

Physica D: Nonlinear Phenomena, 243, (1), 20-31, 2013.1
We study front speeds of curvature and strain G-equations arising in turbulent combustion. These G-equations are HamiltonJacobi type level set partial differential equations (PDEs) with non-coercive Hamiltonians and degenerate nonlinear second order diffusion. The Hamiltonian of a strain G-equation is also non-convex. Numerical computation is performed based on monotone discretization and weighted essentially nonoscillatory (WENO) approximation of transformed G-equations on a fixed periodic domain. The advection field in the computation is a two dimensional Hamiltonian flow consisting of a periodic array of counter-rotating vortices, or cellular flows. Depending on whether the evolution is predominantly in the hyperbolic or parabolic regimes, suitable explicit and semi-implicit time stepping methods are chosen. The turbulent flame speeds are computed as the linear growth rates of large time solutions. A
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@inproceedings{yu-yu2013a,
  title={A numerical study of turbulent flame speeds of curvature and strain G-equations in cellular flows},
  author={Yu-Yu Liu, Jack Xin, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210454657098454},
  booktitle={Physica D: Nonlinear Phenomena},
  volume={243},
  number={1},
  pages={20-31},
  year={2013},
}
Yu-Yu Liu, Jack Xin, and Yifeng Yu. A numerical study of turbulent flame speeds of curvature and strain G-equations in cellular flows. 2013. Vol. 243. In Physica D: Nonlinear Phenomena. pp.20-31. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210454657098454.
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