Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 327, Issue -, Pages 294-316Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.09.029
Keywords
Phase-field; Cahn-Hilliard; Linear; Homopolymer blends; Invariant energy quadratization; Energy stability
Funding
- U.S. National Science Foundation [DMS-1200487, DMS-1418898]
- U.S. Air Force Office of Scientific Research [FA9550-12-1-0178]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1418898] Funding Source: National Science Foundation
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In this paper, we develop a series of efficient numerical schemes to solve the phase field model for homopolymer blends. The governing system is derived from the energetic variational approach of a total free energy, that consists of a nonlinear logarithmic Flory-Huggins potential, and a gradient entropy with a concentration-dependent de-Gennes type coefficient. The main challenging issue to solve this kind of models numerically is about the time marching problem, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to preserve the energy stability at the discrete level. We solve this issue in this paper, by developing the first and second order temporal approximation schemes based on the Invariant Energy Quadratization method, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to a symmetric positive definite linear system to be solved at each time step. The unconditional energy stabilities are further proved. Various numerical simulations of 2D and 3D are presented to demonstrate the stability and the accuracy of the proposed schemes. (C) 2016 Elsevier Inc. All rights reserved.
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