An explicit–implicit time stepping scheme for solidification models

A numerical scheme with hybrid explicit and implicit time stepping in solidification problems is presented. An explicit time stepping scheme is used for solving coupled temperature and concentration fields, while an implicit scheme is used for solving equations of motion. The explicit approach results in a local point-by-point coupling scheme for the temperature and concentration fields that uses constitutive model for back diffusion in solid. The present method offers distinct advantages of simplicity and flexibility in incorporation of micro-scale models, as demonstrated by the use of a back diffusion parameter in the microsegregation model. Results from the present method are compared with those in the literature using a fully implicit method, and they show significant improvement in final macrosegregation prediction.