Vol. 5, No. 2, 2010

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A volume-of-fluid interface reconstruction algorithm that is second-order accurate in the max norm

Elbridge Gerry Puckett

Vol. 5 (2010), No. 2, 199–220
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.

Keywords
volume-of-fluid, interface reconstruction, front reconstruction, piecewise linear interface reconstruction, fronts, two-phase flow, multiphase systems, adaptive mesh refinement, computational fluid dynamics
Mathematical Subject Classification 2000
Primary: 76-04, 65M06, 65M15, 76M20, 76M25
Secondary: 74A50, 94A08, 74S99, 76T99
Milestones
Received: 23 February 2010
Accepted: 14 April 2010
Published: 31 October 2010
Authors
Elbridge Gerry Puckett
University of California, Davis
Department of Mathematics
One Shields Avenue
Davis, CA 95616
United States
http://www.math.ucdavis.edu/