Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 318, Issue -, Pages 1005-1029Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.02.011
Keywords
Phase-field; Fluid-surfactant; Cahn-Hilliard; Energy stability; Ginzburg-Landau; Flory-Huggins
Funding
- U.S. National Science Foundation [DMS-1200487, DMS-1418898, DMS-1521965]
- U.S. Department of Energy [DE-SC0008087-ER6539, DE-SC0016540]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1200487, 1418898] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1521965] Funding Source: National Science Foundation
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In this paper, we consider the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins potential. The resulting system consists of two nonlinearly coupled Cahn-Hilliard type equations. We develop a first and a second order time stepping schemes for this system using the Invariant Energy Quadratization approach; in particular, the system is transformed into an equivalent one by introducing appropriate auxiliary variables and all nonlinear terms are then treated semi-explicitly. Both schemes are linear and lead to symmetric positive definite systems in space at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable in the discrete sense. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes. (C) 2017 Elsevier B.V. All rights reserved.
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