Front-Tracking Finite Element Method for Dendritic Solidification

A two-dimensional finite element method capable of tracking sharp interfaces is developed. The method is based on a fixed mesh of bilinear isoparametric elements and is extremely simple and easy to use. The interfaces are tracked with a set of marker points that define their position at all times. Several different approaches to finding the interface position and velocity are discussed, and their effect on the convergence rate is examined. It is shown through numerical examples that the approximation to the interface position converges with second-order accuracy in two-dimensional problems, as opposed to previously developed finite difference algorithms that are only first-order accurate. The approximation to the interface velocity is shown to be of first order. A number of examples are examined, including several that provide a careful comparison with previously published results.