Abstract
The numerical instabilities associated with solidification and melting processes are mainly due to the transient temperature field in liquid and solid phases and characteristics of the front phase. To prevent these instabilities, a new model for the liquid fraction is proposed in the present article and is based on the analytical Heaviside step function's approximation. The efficiency of the current model is well verified with the numerical simulation of one- and two-dimensional heat conduction problems within regular geometries and is further noticed that the results agree well with the analytical solutions. It is also noted that the proposed model provides more accurate results when compared to the Meshless Local Petrov-Galerkin (MLPG) method and is competent to resolve the above said instabilities. To examine its accuracy for any 2D-arbitrarily-shaped enclosures, a new solidification problem within a more complex geometry was proposed. This problem can be used as a benchmark test for solidification/melting problems. The proposed model was applied to solve this problem and accurate results are obtained. Hence, the previously reported approaches,which are not even able to ensure discrete conservation at the interface, may be replaced by the proposed interface model.