论文标题
ABC和Kolmogorov中G-方程式前速度的半拉格朗日计算，并通过弹道轨道估算
A Semi-Lagrangian Computation of Front Speeds of G-equation in ABC and Kolmogorov Flows with Estimation via Ballistic Orbits
论文作者
论文摘要
Arnold-Beltrami-Childress（ABC）流量和Kolmogorov流量是表现出混乱的流线的三维周期性差异速度场。我们对通过大强度ABC和Kolmogorov流动的湍流燃烧的G-方程感兴趣。我们对ABC和Kolmogorov流的弹道轨道进行定量结构，即在坐标方向上具有最大较大时间渐近速度的那些。得益于G-方程式的最佳控制理论（凸的但非强制性的汉密尔顿 - 雅各比方程），弹道轨道是前速度估计的可允许轨迹。为了研究估计值的紧密度，我们根据半拉格朗日（SL）方案计算G-方程的前速，具有strang分裂和加权本质上是非振荡（WENO）插值。选择时间步长大小，以使Courant数字随着流动强度而倍增。数值结果表明，从流量强度方面的前速度增长率可能接近弹道轨道的分析界限。
The Arnold-Beltrami-Childress (ABC) flow and the Kolmogorov flow are three dimensional periodic divergence free velocity fields that exhibit chaotic streamlines. We are interested in front speed enhancement in G-equation of turbulent combustion by large intensity ABC and Kolmogorov flows. We give a quantitative construction of the ballistic orbits of ABC and Kolmogorov flows, namely those with maximal large time asymptotic speeds in a coordinate direction. Thanks to the optimal control theory of G-equation (a convex but non-coercive Hamilton-Jacobi equation), the ballistic orbits serve as admissible trajectories for front speed estimates. To study the tightness of the estimates, we compute the front speeds of G-equation based on a semi-Lagrangian (SL) scheme with Strang splitting and weighted essentially non-oscillatory (WENO) interpolation. Time step size is chosen so that the Courant number grows sublinearly with the flow intensity. Numerical results show that the front speed growth rate in terms of the flow intensity may approach the analytical bounds from the ballistic orbits.
