A SEMI-LAGRANGIAN COMPUTATION of FRONT SPEEDS of G-EQUATION in ABC and KOLMOGOROV FLOWS with ESTIMATION VIA BALLISTIC ORBITS

Chou Kao, Yu Yu Liu, Jack Xin

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)

摘要

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. First, 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 noncoercive Hamilton-Jacobi equation), the ballistic orbits serve as admissible trajectories for front speed estimates. To study the tightness of the estimates, we compute front speeds of G-equation based on a semi-Lagrangian scheme with Strang splitting and weighted essentially nonoscillatory interpolation. The Semi-Lagrangian scheme is stable when the ratio of time step and spatial grid size is smaller than a positive constant independent of 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.

原文English
頁(從 - 到)107-117
頁數11
期刊Multiscale Modeling and Simulation
20
發行號1
DOIs
出版狀態Published - 2022

All Science Journal Classification (ASJC) codes

  • 化學 (全部)
  • 建模與模擬
  • 生態建模
  • 物理與天文學 (全部)
  • 電腦科學應用

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