A two-dimensional adaptive remeshing method for solving melting and solidification problems with convection

Abstract

Melting and solidification problems in presence of natural convection are known to require high computational resources. Very fine meshes are essential to accurately determine the flow structure and interface position between the different phases. In this work, a time-dependent adaptive remeshing method based on an efficient error estimator is presented. The proposed method greatly reduces the number of mesh elements while maintaining and even enhancing the efficiency of the simulations. A variant of the enthalpy-porosity formulation is used where the different thermo-physical properties between the solid–liquid phases are easily taken into account. A second order mixed finite element formulation for both space and time is employed for solving the momentum and energy equations. The efficiency of the proposed methodology is established by comparing solutions on very fine meshes with those obtained on adapted meshes and with existing experimental and numerical results found in the literature.