A robust method for calculating interface curvature and normal vectors using an extracted local level set

TL;DR

This paper introduces a new robust method for accurately calculating interface curvature and normal vectors in level-set methods, especially during topological changes, improving simulation accuracy in two-phase flows.

Contribution

The paper presents a novel approach that maintains the implicit level-set representation while effectively handling complex interface configurations and topological changes.

Findings

Outperforms standard methods in accuracy during topological changes

Validated on static configurations with good agreement to experiments

Extends naturally to three-dimensional simulations

Abstract

The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit formulation. It is also said that the interface curvature and normal vectors are easily calculated. This last point is not, however, the case in the moments during a topological change, as several authors have already pointed out. Various methods have been employed to circumvent the problem. In this paper, we present a new such method which retains the implicit level-set representation of the surface and handles general interface configurations. It is demonstrated that the method extends easily to 3D. The method is validated on static interface configurations, and then applied to two-phase flow simulations where the method outperforms the standard method and the results agree well with experiments.