A fully decoupled, linear and unconditionally energy stable numerical scheme for a melt-convective phase-field dendritic solidification model

Abstract

We consider in this paper numerical approximations of a melt-convective phase-field dendritic solidification model. A challenging numerical issue for solving this model is how to develop efficient time marching schemes that are not only unconditionally energy stable, but also linear and totally decoupled since the model is a highly coupled nonlinear system. We solve this issue by combining the modified projection scheme for the Navier–Stokes equations, the stabilized-Invariant Energy Quadratization method for the anisotropic phase field equation. Meanwhile, in order to obtain the fully decoupled feature, we introduce an auxiliary intermediate temperature variable to decouple the computation of the temperature from the phase field variable. We prove the unconditional energy stability of the developed scheme and further present various numerical simulations in 2D and 3D to demonstrate the accuracy and stability of the developed scheme.