{"title":"Hybrid Finite Difference Fifth-Order Multi-Resolution WENO Scheme for Hamilton-Jacobi Equations","authors":"Zhenming Wang,Jun Zhu,Linlin Tian, Ning Zhao","doi":"10.4208/cicp.oa-2023-0002","DOIUrl":null,"url":null,"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\none- 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\nmulti-resolution WENO procedures. This hybrid strategy does not contain any human parameters related to specific problems and can identify the troubled grid points\naccurately and automatically. Secondly, a hybrid multi-resolution WENO scheme for\nHamilton-Jacobi equations is developed based on the above discontinuity sensor and a\nsimplified multi-resolution WENO scheme, which yields uniform high-order accuracy\nin smooth regions and sharply resolves discontinuities. Compared with the existing\nmulti-resolution WENO scheme, the method developed in this paper can inherit its\nmany 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\nequations.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4208/cicp.oa-2023-0002","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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.
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.