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

Deng, Xi, Sun, Ziyao, Xie, Bin, Yokoi, Kensuke ORCID: https://orcid.org/0000-0001-7914-6050, Chen, Chungang and Xiao, Feng 2017. A non-oscillatory multi-moment finite volume scheme with boundary gradient switching. Journal of Scientific Computing 72 , pp. 1146-1168. 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:	Publication
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 Verlag
ISSN:	0885-7474
Date of First Compliant Deposit:	9 March 2017
Date of Acceptance:	11 February 2017
Last Modified:	30 Nov 2024 20:15
URI:	https://orca.cardiff.ac.uk/id/eprint/98744

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