Simulating phase transformations by a meshless method with front tracking

A particle-based front tracking method for phase transformation problems is combined with the meshless diffuse approximation method (DAM) and implemented on a two-dimensional unstructured, amorphous grid. The resulting novel method is capable of completely disposing of the grid anisotropy effects common to moving interface problems, as the underlying grid itself has no distinguished direction. The particles track the interface directly and are embedded in the irregular grid by associating each tracking particle with a pair of grid nodes of different phases. This allows for a straightforward treatment of nodes that are subject to a change of phase. The conservation equation at the interface is solved explicitly at the location of the particles. The interface geometry is calculated from the particles' position by a modified local least squares fitting method. The resulting meshless front tracking method is tested on sample solidification problems in one and two dimensions. An excellent match with analytical and published numerical results is found.