Composite finite elements for a phase change model

We present a model and the related discretization for phase change problems. In particular, we are focused on the evaporation of water. The governing equations inside the domains and conditions on the moving interface are derived. Afterward the numerical methods for the discretization are presented. We use a level set method to capture the interface motion and use composite finite elements (CFEs) to solve the required equations in the whole domain. CFEs are a special kind of finite elements, allowing a fast calculation, because they use structured grids and respect the geometry by adapting the basis functions in the neighborhood of an interface or at the domain boundary. For the special construction of CFEs used in this paper, we present a method to take into account Dirichlet boundary conditions on the complicated domain boundary. Also, the method used for the calculation of the interface conditions within the CFE-grid is presented. We tested the Dirichlet boundary condition method for the CFEs by solving an elliptic test problem with a precomputed right-hand side. The phase change discretization is tested by verifying the d(2) law, a widely used test in the phase change and moving boundary context. With the CFE discretization, we are able to solve the full three-dimensional (3D) problem. Afterward we give a short introduction to radio-frequency ablation and present a possibility for integrating the presented phase change model into the simulation of the ablation.