Fixed mesh front-tracking methodology for finite element simulations

A direct front-tracking method using an Eulerian-Lagrangian formulation is developed in two space dimensions. The front-tracking method is general in that it can track any type of interface once its local velocity is specified or has been determined by calculation. The method uses marker points to describe the interface position and tracks the interface evolution on a fixed finite-element mesh, including growth, contraction, splitting and merging. Interfacial conditions are applied directly at the interface position. The method is applied to three scenarios that involve different interface conditions and are based on energy and mass diffusion. The three calculations are for the dendritic solidification of a pure substance, the cellular growth of an alloy, and the Ostwald ripening of silica particles in silicon. Numerical results show that very complicated interface morphologies and topological changes can be simulated properly and efficiently.