A Curvature-Augmented, REA Approach to the Level Set Method

Abstract

When solving a moving interface problem, the interface can be tracked using a variety of methods. The level set method captures the interface as an isocontour of a scalar level set function. The method has many advantages, including the ability to express many geometric quantities, such as the interface curvature, as derivatives of the level set. However, the numerically constructed level set function may not be smooth enough to compute the required derivatives. Furthermore, the method overall is known for having a high sensitivity to numerical dissipation. The former of these two shortfalls is addressed by augmenting the traditional level set equations with an explicitly tracked interface curvature. The curvature is then updated alongside the level set through an additional advection equation. The latter shortfall is addressed by combining a new velocity extension, that better maintains the signed-distance property of the level set, with a reconstruct-evolve-average approach to advancing the advection equations. The new approach is shown to have less mass loss (numerical dissipation) and better accuracy than comparable level set approaches. Three scenarios are investigated: an interface moving according to an external velocity field, an interface moving according to the interface curvature (mean-curvature flow), and the air-water interface of a water drop moving according to the curvature-dependent fluid velocity (surface-tension driven flow).