胞格流中曲率和应变G方程的湍流火焰速度数值研究
A Numerical Study of Turbulent Flame Speeds of Curvature and Strain G-equations in Cellular Flows
AI总结：
通过数值模拟研究湍流燃烧中曲率和应变G方程的火焰前缘速度，发现曲率G方程的湍流火焰速度随胞格流强度增加而增强，而应变G方程的速度先增后减，并在有限强度下熄灭。
摘要：
我们研究了湍流燃烧中出现的曲率和应变G方程的火焰前缘速度。这些G方程是具有非强制哈密顿量和退化非线性二阶扩散的Hamilton-Jacobi型水平集偏微分方程。应变G方程的哈密顿量也是非凸的。数值计算基于单调离散化和变换后的G方程在固定周期域上的加权本质无振荡逼近。计算中的平流场是一个二维哈密顿流，由周期性的反向旋转涡旋阵列或胞格流组成。根据演化主要处于双曲还是抛物区域，选择适当的显式和半隐式时间步进方法。湍流火焰速度被计算为大时间解的线性增长率。提出了一种新的非线性抛物型偏微分方程用于水平集函数的重新初始化，以防止周期域上多束水平集的堆积。我们发现，曲率G方程的湍流火焰速度$s_T$随着胞格流强度$A$的增加而增强，其速率介于无粘和粘性G方程之间。应变G方程的$s_T$在$A$较小时增加，在$A$较大时减小，然后在足够大的有限值$A_{*}$处下降到零。火焰前缘在此临界强度$A_*$处停止传播，并被胞格流熄灭。
英文摘要：
We study front speeds of curvature and strain G-equations arising in turbulent combustion. These G-equations are Hamilton-Jacobi type level set partial differential equations (PDEs) with non-coercive Hamiltonians and degenerate nonlinear second order diffusion. The Hamiltonian of 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 new nonlinear parabolic PDE is proposed for the reinitialization of level set functions to prevent piling up of multiple bundles of level sets on the periodic domain. We found that the turbulent flame speed $s_T$ of the curvature G-equation is enhanced as the intensity $A$ of cellular flows increases, at a rate between those of the inviscid and viscous G-equations. The $s_T$ of the strain G-equation increases in small $A$, decreases in larger $A$, then drops down to zero at a large enough but finite value $A_{*}$. The flame front ceases to propagate at this critical intensity $A_*$, and is quenched by the cellular flow.
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