Phase‐field modelling of solidification microstructure formation using the discontinuous finite element method

Abstract

AbstractThis paper presents a discontinuous Galerkin finite element computational methodology for solving the coupled phase‐field and heat diffusion equations to predict the microstructure evolution during solidification. The phase‐field modelling of microstructure formation is briefly discussed. The discontinuous Galerkin finite element formulation for the phase‐field model systems for solidification microstructure formation is described in detail. Numerical stability is performed using the Neumann method. The accuracy of the discontinuous model is verified by the analytic solution of a simple 1‐D solidification problem. Numerical calculations using the discontinuous finite element phase‐field model have been performed for simulating the complex 2‐D and 3‐D dendrite structures formed in supercooled melts and the results are compared well with those in literature using the finite difference methods. Parallel computing algorithm is presented and results show that the minimization of the intercommunication between microprocessors is the key to increase the effectiveness in parallel computing with the discontinuous finite element phase‐field model for solidification microstructure formation. Copyright © 2006 John Wiley & Sons, Ltd.