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Title: Height-function curvature estimation with arbitrary order on non-uniform Cartesian grids
Author(s): Evrard, Fabien
Denner, Fabian
Wachem, BerendLook up in the Integrated Authority File of the German National Library
Issue Date: 2020
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-389908
Subjects: Curvature
Non-uniform grid
Arbitrary order
Abstract: This paper proposes a height-function algorithm to estimate the curvature of two-dimensional curves and three-dimensional surfaces that are defined implicitly on two-and three-dimensional non-uniform Cartesian grids. It relies on the reconstruction of local heights, onto which polynomial height-functions are fitted. The algorithm produces curva-ture estimates of order N−1anywhere in a stencil of (N+1)d−1heights computed from the volume-fraction data available on a d-dimensional non-uniform Cartesian grid. These estimates are of order Nat the centre of the stencil when it is symmetric about its main axis. This is confirmed by a comprehensive convergence analysis conducted on the errors associated with the application of the algorithm to a fabricated test-curve and test-surface.
Open Access: Open access publication
License: (CC BY-NC-ND 4.0) Creative Commons Attribution NonCommercial NoDerivatives 4.0(CC BY-NC-ND 4.0) Creative Commons Attribution NonCommercial NoDerivatives 4.0
Sponsor/Funder: OVGU-Publikationsfonds 2020
Journal Title: Journal of computational physics: X
Publisher: Elsevier
Publisher Place: Amsterdam
Volume: 7
Issue: 2020
Original Publication: 10.1016/j.jcpx.2020.100060
Page Start: 1
Page End: 15
Appears in Collections:Fakultät für Verfahrens- und Systemtechnik (OA)

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