Hybrid Finite Difference Fifth-Order Multi-Resolution WENO Scheme for Hamilton-Jacobi Equations

IF 2.6 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Computational Physics Pub Date : 2024-04-01 DOI:10.4208/cicp.oa-2023-0002
Zhenming Wang,Jun Zhu,Linlin Tian, Ning Zhao
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Abstract

In this paper, a fifth-order hybrid multi-resolution weighted essentially non-oscillatory (WENO) scheme in the finite difference framework is proposed for solving one- and two-dimensional Hamilton-Jacobi equations. Firstly, a new discontinuity sensor is designed based on the extreme values of the highest degree polynomial in the multi-resolution WENO procedures. This hybrid strategy does not contain any human parameters related to specific problems and can identify the troubled grid points accurately and automatically. Secondly, a hybrid multi-resolution WENO scheme for Hamilton-Jacobi equations is developed based on the above discontinuity sensor and a simplified multi-resolution WENO scheme, which yields uniform high-order accuracy in smooth regions and sharply resolves discontinuities. Compared with the existing multi-resolution WENO scheme, the method developed in this paper can inherit its many advantages and is more efficient. Finally, some benchmark numerical experiments are performed to demonstrate the performance of the presented fifth-order hybrid multi-resolution WENO scheme for one- and two-dimensional Hamilton-Jacobi equations.
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针对汉密尔顿-雅可比方程的混合有限差分五阶多分辨率 WENO 方案
本文提出了一种有限差分框架下的五阶混合多分辨率加权本质非振荡(WENO)方案,用于求解一维和二维汉密尔顿-雅可比方程。首先,根据多分辨率 WENO 程序中最高多项式的极值设计了一种新的不连续传感器。这种混合策略不包含任何与具体问题相关的人为参数,可以准确自动地识别问题网格点。其次,基于上述非连续性传感器和简化的多分辨率 WENO 方案,针对哈密尔顿-雅可比方程开发了一种混合多分辨率 WENO 方案,在平滑区域获得均匀的高阶精度,并显著解决非连续性问题。与现有的多分辨率 WENO 方案相比,本文开发的方法继承了它的许多优点,而且更加高效。最后,通过一些基准数值实验证明了本文提出的五阶混合多分辨率 WENO 方案在一维和二维 Hamilton-Jacobiequestions 中的性能。
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来源期刊
Communications in Computational Physics
Communications in Computational Physics 物理-物理:数学物理
CiteScore
4.70
自引率
5.40%
发文量
84
审稿时长
9 months
期刊介绍: Communications in Computational Physics (CiCP) publishes original research and survey papers of high scientific value in computational modeling of physical problems. Results in multi-physics and multi-scale innovative computational methods and modeling in all physical sciences will be featured.
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