Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Numerical analysis of a continuum model of phase transition
SIAM Journal on Numerical Analysis
The dynamics of nucleation for the Cahn-Hilliard equation
SIAM Journal on Applied Mathematics
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Computation of multiphase systems with phase field models
Journal of Computational Physics
Conservative multigrid methods for Cahn-Hilliard fluids
Journal of Computational Physics
Journal of Computational Physics
A multigrid solver for phase field simulation of microstructure evolution
Mathematics and Computers in Simulation
Three-dimensional, fully adaptive simulations of phase-field fluid models
Journal of Computational Physics
Computers & Mathematics with Applications
A quantitative comparison between C0 and C1 elements for solving the Cahn-Hilliard equation
Journal of Computational Physics
Hi-index | 31.46 |
We present a nonstiff, fully adaptive mesh refinement-based method for the Cahn-Hilliard equation. The method is based on a semi-implicit splitting, in which linear leading order terms are extracted and discretized implicitly, combined with a robust adaptive spatial discretization. The fully discretized equation is written as a system which is efficiently solved on composite adaptive grids using the linear multigrid method without any constraint on the time step size. We demonstrate the efficacy of the method with numerical examples. Both the transient stage and the steady state solutions of spinodal decompositions are captured accurately with the proposed adaptive strategy. Employing this approach, we also identify several stationary solutions of that decomposition on the 2D torus.