A volume-of-fluid interface reconstruction algorithm that is second-order accurate in the max norm

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.