A new fifth order finite difference WENO scheme for Hamilton-Jacobi equations
A new fifth order finite difference WENO scheme for Hamilton-Jacobi equations
复制标题
Hamilton-Jacobi方程的新五阶有限差分WENO格式
DOI：
10.1002/num.22133
复制
发表时间：
2017
影响因子：
3.9
通讯作者：
Qiu Jianxian
中科院分区：
文献类型：
--
作者：
Zhu Jun;Qiu Jianxian
在（Zhu and Qiu，J Comput Phys 318（2016），110-121）的这篇续论文中，设计了一种新的五阶有限差分加权基本无振荡（韦诺）格式来近似汉密尔顿-雅可比方程的粘性数值解。这种新的韦诺格式与Jiang和Peng（SIAM J Sci Comput 21（2000），2126-2143）提出的经典五阶韦诺格式在空间节点数相同的情况下，可以得到更小的绝对截断误差，在光滑区域获得相同量级的精度，同时避免了间断附近的虚假振荡。这种新的韦诺格式是一个四阶精度多项式和两个线性多项式的凸组合，在空间重建过程中的韦诺类型的方式。将三个多项式的线性权人为地设置为任意随机的正常数，并提出了新的非线性权，以保持格式在光滑区域的精度，避免伪振荡，同时在非光滑区域保持尖锐的不连续过渡.与Jiang和Peng（SIAM J Sci Comput 21（2000），2126-2143）提出的经典韦诺方案相比，这种新的WENO方案的主要优点是它的效率、鲁棒性和易于实现到高维。大量的数值试验表明，新的第五韦诺格式的能力。© 2016 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq 33：1095-1113，2017
In this continuing paper of (Zhu and Qiu, J Comput Phys 318 (2016), 110–121), a new fifth order finite difference weighted essentially non‐oscillatory (WENO) scheme is designed to approximate the viscosity numerical solution of the Hamilton‐Jacobi equations. This new WENO scheme uses the same numbers of spatial nodes as the classical fifth order WENO scheme which is proposed by Jiang and Peng (SIAM J Sci Comput 21 (2000), 2126–2143), and could get less absolute truncation errors and obtain the same order of accuracy in smooth region simultaneously avoiding spurious oscillations nearby discontinuities. Such new WENO scheme is a convex combination of a fourth degree accurate polynomial and two linear polynomials in a WENO type fashion in the spatial reconstruction procedures. The linear weights of three polynomials are artificially set to be any random positive constants with a minor restriction and the new nonlinear weights are proposed for the sake of keeping the accuracy of the scheme in smooth region, avoiding spurious oscillations and keeping sharp discontinuous transitions in nonsmooth region simultaneously. The main advantages of such new WENO scheme comparing with the classical WENO scheme proposed by Jiang and Peng (SIAM J Sci Comput 21 (2000), 2126–2143) are its efficiency, robustness and easy implementation to higher dimensions. Extensive numerical tests are performed to illustrate the capability of the new fifth WENO scheme. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1095–1113, 2017