Height-function curvature estimation with arbitrary order on non-uniform Cartesian grids

• Main Authors: Fabien Evrard, Fabian Denner, Berend van Wachem
• Format: Article
• Language: English
• Published: Elsevier 2020-06-01
• Series: Journal of Computational Physics: X
• Subjects: Curvature; Volume-of-fluid; Height-function; Non-uniform grid; Arbitrary order
• Online Access: http://www.sciencedirect.com/science/article/pii/S2590055220300123

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.