{"title":"An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions","authors":"Li Chen, Ruo Li, Feng Yang","doi":"10.4208/csiam-am.2020-0017","DOIUrl":null,"url":null,"abstract":"We proposed a piecewise quadratic reconstruction method, which is in an integrated style, for finite volume schemes to scalar conservation laws. This quadratic reconstruction is parameter-free, is of third-order accuracy for smooth functions, and is flexible on structured and unstructured grids. The finite volume schemes with the new reconstruction satisfy a local maximum principle. Numerical examples are presented to show that the proposed schemes with a third-order Runge-Kutta method attain the expected order of accuracy.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2017-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/csiam-am.2020-0017","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 2
Abstract
We proposed a piecewise quadratic reconstruction method, which is in an integrated style, for finite volume schemes to scalar conservation laws. This quadratic reconstruction is parameter-free, is of third-order accuracy for smooth functions, and is flexible on structured and unstructured grids. The finite volume schemes with the new reconstruction satisfy a local maximum principle. Numerical examples are presented to show that the proposed schemes with a third-order Runge-Kutta method attain the expected order of accuracy.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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