Abstract
In a previous article in this journal the author proved that, given a square grid of side covering a two times continuously differentiable simple closed curve in the plane, one can construct a pointwise second-order accurate piecewise linear approximation to from just the volume fractions due to in the grid cells. In the present article the author proves a sufficient condition for to be a second-order accurate approximation to in the max norm is must be bounded above by , where is the maximum magnitude of the curvature of . This constraint on is solely in terms of an intrinsic property of the curve , namely , which is invariant under rotations and translations of the grid. It is also far less restrictive than the constraint presented in the previous article. An important consequence of the proof in the present article is that the max norm of the difference depends linearly on .
Citation
Elbridge Puckett. "Second-order accuracy of volume-of-fluid interface reconstruction algorithms II: An improved constraint on the cell size." Commun. Appl. Math. Comput. Sci. 8 (1) 123 - 158, 2013. https://doi.org/10.2140/camcos.2013.8.123
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