Recent advances, trends and new perspectives via enthalpy‐based finite element formulations for applications to solidification problems

The present paper describes recent advances and trends in finite element developments and applications for solidification problems. In particular, in comparison to traditional methods of approach, new enthalpy‐based architectures based on a generalized trapezoidal family of representations are presented which provide different perspectives, physical interpretation and solution architectures for effective numerical simulation of phase change processes encountered in solidification problems. Various numerical test models are presented and the results support the proposition for employing such formulations for general phase change applications.