A Semi-implicit Gradient Augmented Level Set Method

Here a semi-implicit formulation of the gradient augmented level set method is presented. The method is a hybrid Lagrangian–Eulerian method that may be easily applied in two or three dimensions. By tracking both the level set function and the gradient of the level set function, highly accurate descriptions of a moving interface can be formed. Stability is enhanced by the addition of a smoothing term to the gradient augmented level set equations. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. Sample results presented in both two and three dimensions demonstrate the applicability of the scheme. The influence of the smoothing term on stability and accuracy is also investigated.