Splitting schemes for phase-field models

摘要

In this paper, we consider several splitting schemes for unsteady problems for the most common phase-field models. The fully implicit discretization of such problems would yield at each time step a nonlinear problem that involves second- or higher-order spatial operators. We derive new factorization schemes that linearize the equations and split the higher-order operators as a product of second-order operators that can be further split direction-wise. We prove the unconditional stability of the first-order schemes for the case of constant mobility. If the spatial discretization uses Cartesian grids, the most efficient schemes are Locally One Dimensional (LOD). We validate our theoretical analysis with 2D numerical examples.