An Interface-Fitted Finite Element Level Set Method with Application to Solidification and Solvation (Communications in Computational Physics, 2011)
A new finite element level set method is developed to simulate the interfacemotion. The normal velocity of the moving interface can depend on both the local geometry,such as the curvature, and the external force such as that due to the flux fromboth sides of the interface of a material whose concentration is governed by a diffusionequation. The key idea of the method is to use an interface-fitted finite element mesh.Such an approximation of the interface allows an accurate calculation of the solutionto the diffusion equation. The interface-fitted mesh is constructed from a base mesh, auniform finite element mesh, at each time step to explicitly locate the interface and separateregions defined by the interface. Several new level set techniques are developedin the framework of finite element methods. These include a simple finite elementmethod for approximating the curvature, a new method for the extension of normalvelocity, and a finite element least-squares method for the reinitialization of level setfunctions. Application of the method to the classical solidification problem capturesthe dendrites. The method is also applied to the molecular solvation to determineoptimal solute-solvent interfaces of solvation systems.