A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method

By Chun Liu, Jie Shen. 2003

665 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/95b56e0702419cbea785f4754bffb564e76ac4e6

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Citations in the corpus

On a diffuse interface model for a two-phase flow of compressible viscous fluids (2008, methodology): “A similar model for incompressible fluids was studied by Boyer [6], Liu and Shen [19], Starovoitov [22], and the first author [1].”
An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation (2012, background): “1c), then the following energy identity holds [1, 12], dE(u) dt +‖∇μ‖(2) =0, (2.”
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows (2017, neutral): “The Allen-Cahn [2] and Cahn-Hilliard equations [13, 14], are widely used in the study of interfacial dynamics [2, 62, 4, 42, 46, 52, 53, 76, 1].”
Study of a three component Cahn-Hilliard flow model (2006, neutral): “1, see also [8,22]) when only two phases are present in the mixture.”
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids (2005, methodology): “All rights reserved. eywords: Phase-field method; Interfacial dynamics; Film drainage; van der Waals force; Disjoining pressure; Dynamic interfacial tension .”
Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows (2010, neutral): “, for instance, [15]): d dt ∫”
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes (2004, methodology): “In [28,29], we employed numerical methods to simulate the interaction of the flow field with the free vesicles where the surface energy consists only the surface area (which gives rise to the surface tension in the momentum equations).”
Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows (2015, background): “[22]), one can derive ρ(ut + (u · ∇)u) = ∇ · (μD(u)− pI − λ∇φ ⊗∇φ), (2.”
Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, background): “We refer the readers to [43, 27, 28] and references therein.”
Phase-Field Models for Multi-Component Fluid Flows (2012, methodology): “The phase-field is defined to be either the difference between [73] or the fraction of one of [56] the concentrations of the two mixtures φ= m1−m2 m1+m2 , c= m1 m1+m2 , (2.”
A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “This approach has been successfully applied to derive complex hydrodynamic systems in fluid dynamics, liquid crystals, electrokinetics, visco-elasticity, reaction-diffusion process and so on, we refer to [46, 47, 107, 120, 126, 127, 165, 170, 177, 180] and the references cited therein.”
Isogeometric analysis of the Cahn–Hilliard phase-field model (2008, background): “dealing with higher-order operators on very simple geometries include finite differences (see applications to the Cahn–Hilliard equation in [35,69]) and spectral approximations (solutions to the Cahn– Hilliard equation can be found in [58,60,78,79]).”
Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing (2006, background): “As is well known, the Cahn– Hilliard dynamics is conservative in the sense that R /dX remains a constant in the absence of boundary fluxes [7].”
A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system (2012, neutral): “The fluid dynamics is described by the Navier–Stokes–Cahn–Hilliard (NSCH) equations [3–5,11–16]:”
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations (2010, background): “Nowadays, the Allen-Cahn and Cahn-Hilliard equations have been widely used in many complicated moving interface problems in materials science and fluid dynamics through a phase-field approach (cf., for instance, [19] [7] [2] [6] [17] [27] [25] [9]).”