An alternating Crank-Nicolson method for the numerical solution of the phase-field equations using adaptive moving meshes

Abstract

An alternating Crank-Nicolson method is proposed for the numerical solution of the phase-field equations on a dynamically adaptive grid, which automatically leads to two decoupled algebraic subsystems, one is linear and the other is semilinear. The moving mesh strategy is based on the approach proposed by Li et al. (J. Comput. Phys. 2001; 170:562-588) to separate the mesh-moving and partial differential equation evolution. The phase-field equations are discretized by a finite volume method in space, and the mesh-moving part is realized by solving the conventional Euler-Lagrange equations with the standard gradient-based monitors. The algorithm is computationally efficient and has been successfully used in numerical simulations. Copyright © 2007 John Wiley & Sons, Ltd.