L1‐type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton‐Jacobi equations,International Journal for Numerical Methods in Fluids

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L1‐type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton‐Jacobi equations
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-05-10 , DOI: 10.1002/fld.4855
Samala Rathan ₁

Affiliation

This article presents an improved fifth‐order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton‐Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹‐norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one‐ and two‐dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.

中文翻译：

基于L1型光滑度指标的Hamilton-Jacobi方程的加权基本非振荡方案

本文提出了一种改进的五阶有限差分加权基本非振荡（WENO）方案来解决Hamilton-Jacobi方程。引入了一种新型的非线性权重，在每个局部模具上构造局部平滑度指示器，这些指示器借助L ¹范数的广义未除差来进行测量。还可以通过线性组合的局部测量来构建一种新颖的全局平滑度测量。在一维和二维中进行了数值实验，以证明所提出方案的性能增强，分辨率提高，数值准确性，并将其与经典WENO方案进行了比较。

更新日期：2020-05-10

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