Discontinuous Finite Element Phase-Field Modeling of Solidification Microstructure Formation

A discontinuous Galerkin finite element computational methodology is presented for the solution of the coupled phase-field and heat conduction equations for modeling microstructure evolution during solidification. The details of the discontinuous formulation and the solution procedures are given. A major difference between the current method and those used in the literatures is the application of higher-order localized formulation and unstructured mesh, which holds a great promise in both parallel computing and adaptive meshing. The accuracy of the discontinuous model is checked with the analytic solution for a simple 1-D solidification problem. Numerical simulations and selected results are given for more complex 2-D dendrite structures formed during solidification. The calculated results are consistent with those reported in literature.