The Semi Implicit Gradient Augmented Level Set Method

TL;DR

This paper introduces a semi-implicit gradient augmented level set method that accurately tracks moving interfaces in multiple dimensions, enabling detailed analysis of curvature-driven interface evolution with demonstrated stability.

Contribution

It presents a novel semi-implicit hybrid Lagrangian-Eulerian scheme that tracks both level set and gradient for improved accuracy in interface evolution modeling.

Findings

The method achieves high accuracy in interface tracking.

Numerical experiments confirm the scheme's stability.

Convergence and accuracy results are provided.

Abstract

Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving interface. The result is a hybrid Lagrangian-Eulerian method that may be easily applied in two or three dimensions. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. In this work the algorithm, convergence and accuracy results are presented. Several numerical experiments in both two and three dimensions demonstrate the stability of the scheme.