Tracking of solidification profile during continuous casting by a spline based collocation algorithm

A novel numerical framework has been developed which comprises of a cubic spline based collocation method to determine the solidification profile (front) during continuous casting process. The basis function chosen for the collocation method is a cubic spline interpolation function. An iterative solution methodology has been developed to track the solidification profile for copper strand of rectangular transverse section for different casting speeds. It is based on enthalpy conservation criteria at the solidification interface found to be in good agreement with the experimental data available in literature. The spline based collocation algorithm is found to be advantageous for solidification front tracking process as a good spatial derivative approximation can be achieved incorporating simple modelling philosophy which is numerically efficient and computationally cost effective.