The Semi Implicit Gradient Augmented Level Set Method

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.Comment: 19 Pages, 14 Figure

Continuous and Discontinuous Finite Element Methods for Coupled Surface-Subsurface Flow and Transport Problems

A weak formulation of the coupled problem of flow and transport is discretized and analyzed numerically. The flow problem is characterized by the Navier-Stokes (or Stokes) equations coupled by Darcy equations. The velocity field is obtained by couplings of finite element and discontinuous Galerkin methods. The concentration equation is solved by an improved discontinuous Galerkin method. Convergence of the schemes is obtained. Numerical examples show the robustness of the method for heterogeneous and fractured porous media