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2010 A volume-of-fluid interface reconstruction algorithm that is second-order accurate in the max norm
Elbridge Puckett
Commun. Appl. Math. Comput. Sci. 5(2): 199-220 (2010). DOI: 10.2140/camcos.2010.5.199

Abstract

In an article recently published in this journal the author proved there exists a two-dimensional, volume-of-fluid interface reconstruction method that is second-order accurate in the max norm. However, that article did not include an example of such an algorithm. This article contains a description of a two-dimensional, volume-of-fluid interface reconstruction method that is second-order accurate in the max norm, provided the curve that one is reconstructing is two times continuously differentiable and the length of the sides of the square grid cells is less than a constant divided by the maximum of the absolute value of the curvature of the interface. A computation made with this algorithm is presented that demonstrates the convergence rate is second-order, as expected.

Citation

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Elbridge Puckett. "A volume-of-fluid interface reconstruction algorithm that is second-order accurate in the max norm." Commun. Appl. Math. Comput. Sci. 5 (2) 199 - 220, 2010. https://doi.org/10.2140/camcos.2010.5.199

Information

Received: 23 February 2010; Accepted: 14 April 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1277.76064
MathSciNet: MR2765383
Digital Object Identifier: 10.2140/camcos.2010.5.199

Subjects:
Primary: 65M06, 65M15, 76-04, 76M20, 76M25
Secondary: 74A50, 74S99, 76T99, 94A08

Rights: Copyright © 2010 Mathematical Sciences Publishers

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