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
