The Semi Implicit Gradient Augmented Level Set Method
This work offers a more stable and accurate numerical method for simulating moving interfaces, benefiting computational physics and engineering applications involving interface evolution.
The paper presents a semi-implicit formulation of the gradient augmented level set method, which provides accurate subgrid information for moving interfaces. The method is stable and accurate in 2D and 3D, with demonstrated convergence for curvature-driven flows.
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.