Height-function curvature estimation with arbitrary order on non-uniform Cartesian grids
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-fun...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020-06-01
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| Series: | Journal of Computational Physics: X |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590055220300123 |
| Summary: | 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 curvature estimates of order N−1 anywhere in a stencil of (N+1)d−1 heights computed from the volume-fraction data available on a d-dimensional non-uniform Cartesian grid. These estimates are of order N at 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. |
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| ISSN: | 2590-0552 |