Discontinuous Finite-Element Phase-Field Modeling of Polycrystalline Grain Growth with Convection

This paper presents a discontinuous finite-element computational framework for the numerical modeling of polycrystalline microstructure formation during solidification processing, taking into account the effect of convection. An important aspect of the discontinuous formulation is that the interelement continuity is relaxed for all the field variables or more precisely the continuity across the elements is weakly enforced, rather than strongly enforced as done in conventional finite-element methods. Because of this local nature, the discontinuous finite-element method enjoys certain advantages over the traditional finite difference and finite-element methods, in particular, for large scale numerical simulations of physical phenomena in thermal and fluids systems. The solution procedure involves an element-by-element iterative sweep. The discontinuous finite-element formulation is presented for a fully coupled set of nonlinear equations including the Navier-Stokes equations, the phase-field equation, the thermal equation, and the crystal orientation equation, which describe the physical phenomena associated with solidification processing. Both single grain and polygrain models are considered. Numerical results are presented that illustrate the effect of convection on the microstructure formation during polycrystalline solidification.