An Adaptive Mesh Refined Gradient-Augmented Level Set Method

The Gradient-Augmented Level Set method (GA-LS) was introduced at the 62$^{nd}$ annual APS-DFD meeting by Nave et al. (arXiv:0905.3409). Leveraging the optimal locality and unconditional stability of the method, we present a natural extension to adaptive quad-tree meshes. The new method possesses many desirable features such as improved mass conservation, reduced computational effort, and is, due to the optimal locality property of the underlying GA-LS, very easy to implement. Several key benchmark tests will be presented to help demonstrate the benefits of the approach, and the overall simplicity of the algorithm.