Calculation of interface curvature with the level-set method

TL;DR

This paper proposes an improved discretization scheme for calculating interface curvature and normal vectors in the level-set method, especially effective during topological changes like drop collisions, enhancing robustness over standard methods.

Contribution

It introduces a new discretization scheme for curvature and normal vector calculation in the level-set method that better handles topological changes.

Findings

The improved scheme is more robust during topological changes.

It performs better than standard discretization in collision scenarios.

The method is easy to implement into existing codes.

Abstract

The level-set method is a popular method for interface capturing. One of the advantages of the level-set method is that the curvature and the normal vector of the interface can be readily calculated from the level-set function. However, in cases where the level-set method is used to capture topological changes, the standard discretization techniques for the curvature and the normal vector do not work properly. This is because they are affected by the discontinuities of the signed-distance function half-way between two interfaces. This article addresses the calculation of normal vectors and curvatures with the level-set method for such cases. It presents a discretization scheme that is relatively easy to implement in to an existing code. The improved discretization scheme is compared with a standard discretization scheme, first for a case with no flow, then for a case where two drops collide in a shear flow. The results show that the improved discretization yields more robust calculations in areas where topological changes are imminent.