High-order time-marching reinitialization for regional level-set functions
High-order time-marching reinitialization for regional level-set functions
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DOI：
10.1016/j.jcp.2017.10.054
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发表时间：
2018-02
期刊：
影响因子：
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通讯作者：
Shucheng Pan;Xiuxiu Lyu;Xiangyu Y. Hu;N. Adams
中科院分区：
文献类型：
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作者：
Shucheng Pan;Xiuxiu Lyu;Xiangyu Y. Hu;N. Adams
在这项工作中，时间推进重新初始化方法被扩展到计算无符号距离函数的多区域系统，包括任意数量的区域。高阶和界面的保持是通过应用一个简单的映射，将区域水平集函数的水平集函数和高阶两步重新初始化方法，这是一个组合的最近点查找过程和HJ-WENO计划。最近点寻找过程中的三维收敛失败，解决了采用建议的多路口处理和方向优化算法。简单的测试案例表明，我们的方法具有四阶精度重新初始化的区域水平集函数，并严格满足接口保持性质。重新初始化的结果更复杂的情况下，随机生成的图表显示的能力，我们的方法为任意数量的区域N，与独立的N的计算工作。所提出的方法已被应用到动态接口与不同类型的流，结果表明，高精度和鲁棒性。
In this work, the time-marching reinitialization method is extended to compute the unsigned distance function in multi-region systems involving arbitrary number of regions. High order and interface preservation are achieved by applying a simple mapping that transforms the regional level-set function to the level-set function and a high-order two-step reinitialization method which is a combination of the closest point finding procedure and the HJ-WENO scheme. The convergence failure of the closest point finding procedure in three dimensions is addressed by employing a proposed multiple junction treatment and a directional optimization algorithm. Simple test cases show that our method exhibits 4th-order accuracy for reinitializing the regional level-set functions and strictly satisfies the interface-preserving property. The reinitialization results for more complex cases with randomly generated diagrams show the capability our method for arbitrary number of regions N, with a computational effort independent of N. The proposed method has been applied to dynamic interfaces with different types of flows, and the results demonstrate high accuracy and robustness.