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dc.contributor.authorZhang, Dien
dc.contributor.authorJiang, Chunboen
dc.contributor.authorLiang, Dongfangen
dc.contributor.authorCheng, Liangen
dc.date.accessioned2015-09-08T10:57:56Z
dc.date.available2015-09-08T10:57:56Z
dc.date.issued2015-09-04en
dc.identifier.citationJournal of Computational Physics 2015, 302, 114-154. doi: 10.1016/j.jcp.2015.08.042en
dc.identifier.issn0021-9991
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/250531
dc.description.abstractThis paper presents an extensive review of most of the existing TVD schemes found in literature that are based on the One-step Time-space-coupled Unsteady TVD criterion (OTU-TVD), the Multi-step Time-space-separated Unsteady TVD criterion (MTU-TVD) and the Semi-discrete Steady-state TVD criterion (SS-TVD). The design principles of these schemes are examined in detail. It is found that the selection of appropriate flux-limiters is a key design element in developing these schemes. Different flux-limiter forms (CFL-dependent or CFL-independent, and various limiting criteria) are shown to lead to different performances in accuracy and convergence. Furthermore, a refined SS-TVD flux-limiter, referred to henceforth as TCDF (Third-order Continuously Differentiable Function), is proposed for steadystate calculations based on the review. To evaluate the performance of the newly proposed scheme, many existing classical SS-TVD limiters are compared with the TCDF in eight two-dimensional test cases. The numerical results clearly show that the TCDF results in an improved overall performance.
dc.description.sponsorshipThe authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51279082 and 51511130073) and the support from Australian Research Council through a Discovery Grant (Project ID: DP110105171).
dc.languageEnglishen
dc.language.isoenen
dc.publisherElsevier
dc.subjecttotal variation diminishingen
dc.subjecthigh resolution schemeen
dc.subjectnormalized variable diagramen
dc.subjectconvection boundedness criterionen
dc.subjectconvection discretizationen
dc.subjectflux limiteren
dc.titleA review on TVD schemes and a refined flux-limiter for steady-state calculationsen
dc.typeArticle
dc.description.versionThis is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jcp.2015.08.042en
prism.endingPage154
prism.publicationDate2015en
prism.publicationNameJournal of Computational Physicsen
prism.startingPage114
prism.volume302en
rioxxterms.versionofrecord10.1016/j.jcp.2015.08.042en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2015-09-04en
dc.identifier.eissn1090-2716
rioxxterms.typeJournal Article/Reviewen
rioxxterms.freetoread.startdate2017-09-04


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