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A non-oscillatory multi-moment finite volume scheme with boundary gradient switching

Deng, Xi, Sun, Ziyao, Xie, Bin, Yokoi, Kensuke, Chen, Chungang and Xiao, Feng 2017. A non-oscillatory multi-moment finite volume scheme with boundary gradient switching. Journal of Scientific Computing 10.1007/s10915-017-0392-0

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Abstract

In this work we propose a new formulation for high-order multi-moment constrained finite volume (MCV) method. In the one-dimensional building-block scheme, three local degrees of freedom (DOFs) are equidistantly defined within a grid cell. Two candidate polynomials for spatial reconstruction of third-order are built by adopting one additional constraint condition from the adjacent cells, i.e. the DOF at middle point of left or right neighbour. A boundary gradient switching (BGS) algorithm based on the variation-minimization principle is devised to determine the spatial reconstruction from the two candidates, so as to remove the spurious oscillations around the discontinuities. The resulted non-oscillatory MCV3-BGS scheme is of fourth-order accuracy and completely free of case-dependent ad hoc parameters. The widely used benchmark tests of one- and two-dimensional scalar and Euler hyperbolic conservation laws are solved to verify the performance of the proposed scheme in this paper. The MCV3-BGS scheme is very promising for the practical applications due to its accuracy, non-oscillatory feature and algorithmic simplicity.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Engineering
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: Multi-moment methodFinite volume methodVariation-minimization principleNon-oscillatory schemeHigh-order schemeLocal reconstruction
Publisher: Springer
ISSN: 0885-7474
Date of First Compliant Deposit: 9 March 2017
Date of Acceptance: 11 February 2017
Last Modified: 24 Apr 2018 21:48
URI: http://orca-mwe.cf.ac.uk/id/eprint/98744

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