Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
Xiaofeng Yang,Daozhi Han +1 more
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TLDR
A series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model based on the first order Euler method, second order backward differentiation formulas and the second order Crank-Nicolson method are developed.About:
This article is published in Journal of Computational Physics.The article was published on 2017-02-01 and is currently open access. It has received 146 citations till now. The article focuses on the topics: Euler method & Linear system.read more
Citations
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The scalar auxiliary variable (SAV) approach for gradient flows
TL;DR: Numerical results are presented to show that the accuracy and effectiveness of the SAV approach over the existing methods are superior.
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Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
TL;DR: First and second order temporal approximation schemes based on the “Invariant Energy Quadratization” method are developed, where all nonlinear terms are treated semi-explicitly, leading to a symmetric positive definite linear system to be solved at each time step.
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Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
TL;DR: This paper develops a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method, and proves that all proposed schemes are unconditionally energy stable.
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Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method
TL;DR: In this paper, a set of first-and second-order temporal approximation schemes based on a novel "Invariant Energy Quadratization" approach is presented. But the scheme is not energy stable.
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Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach
TL;DR: In this article, the authors proposed a semi-discrete scheme for phase field dendritic crystal growth, which is derived from the variation of a free energy functional, consisting of a temperature dependent bulk potential and a conformational entropy with a gradient-dependent anisotropic coefficient.
References
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Diffuse-interface methods in fluid mechanics
TL;DR: Issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids are addressed.
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Hydrodynamic fluctuations at the convective instability
Jack Swift,P. C. Hohenberg +1 more
TL;DR: In this article, the effects of thermal fluctuations on the convective instability were considered, and it was shown that the Langevin equations for hydrodynamic fluctuations are equivalent, near the instability, to a model for the crystallization of a fluid in equilibrium.
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Regular Article: Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling
TL;DR: In this article, the Navier-Stokes equations are modified by the addition of the continuum forcing [emailprotected]?->@f, where C is the composition variable and @f is C's chemical potential.
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Quasi–incompressible Cahn–Hilliard fluids and topological transitions
John Lowengrub,Lev Truskinovsky +1 more
TL;DR: In this article, a physically motivated regularization of the Euler equations is proposed to allow topological transitions to occur smoothly, where the sharp interface is replaced by a narrow transition layer across which the fluids may mix.
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A diffuse-interface method for simulating two-phase flows of complex fluids
TL;DR: In this paper, the authors proposed a diffuse-interface approach to simulating the flow of two-phase systems of microstructured complex fluids, where the energy law of the system guarantees the existence of a solution.