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dc.contributor.authorShen, Hua
dc.contributor.authorParsani, Matteo
dc.date.accessioned2021-04-14T06:19:47Z
dc.date.available2021-04-14T06:19:47Z
dc.date.issued2021-04-09
dc.identifier.urihttp://hdl.handle.net/10754/668735
dc.description.abstractWe propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation element and solution element (CESE) scheme. On every cell, the solution is approximated by a Pth order polynomial of which all the DOFs are stored and updated separately. The cell average is updated by a classical finite volume scheme which is constructed based on space-time staggered meshes such that the fluxes are continuous across the interfaces of the adjacent control volumes and, therefore, the local Riemann problem is bypassed. The kth order spatial derivatives are updated by a central difference of (k-1)th order spatial derivatives at cell vertices. All the space-time information is calculated by the Cauchy-Kovalewski procedure. By doing so, the schemes are able to achieve arbitrarily uniform spacetime high order on a super-compact stencil with only one explicit time step. In order to capture discontinuities without spurious oscillations, a weighted essentially non-oscillatory (WENO) type limiter is tailor-made for the schemes. The limiter preserves the compactness and high order accuracy of the schemes. The accuracy, robustness, and efficiency of the schemes are verified by several numerical examples of scalar conservation laws and the compressible Euler equations.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2104.04347.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectcompact scheme
dc.subjectcentral scheme
dc.subjectCESE scheme
dc.subjecthigh-order scheme
dc.subjectfinite volume scheme
dc.subjecthyperbolic conservation laws
dc.titleA class of high-order weighted compact central schemes for solving hyperbolic conservation laws
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionSchool of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
dc.identifier.arxivid2104.04347
kaust.personParsani, Matteo
refterms.dateFOA2021-04-14T06:20:15Z


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