Numerical schemes for a three component Cahn-Hilliard model
ESAIM: M2AN, 45 4 (2011) 697-738
Published online: 2010-12-10
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Auxiliary relaxation method to derive thermodynamically consistent phase field models with constraints and structure preserving numerical approximations
Qi Hong, Zengyan Zhang and Jia ZhaoJournal of Computational Physics 522 113598 (2025)
https://doi.org/10.1016/j.jcp.2024.113598
A positivity-preserving, second-order energy stable and convergent numerical scheme for a ternary system of macromolecular microsphere composite hydrogels
Lixiu Dong, Cheng Wang and Zhengru ZhangJournal of Computational and Applied Mathematics 462 116463 (2025)
https://doi.org/10.1016/j.cam.2024.116463
Hybrid hydrodynamic models for active elastic particles driven by self-generated force couples
Qi Hong and Qi WangPhysics of Fluids 37 (3) (2025)
https://doi.org/10.1063/5.0239793
An Enhanced and Highly Efficient Semi‐Implicit Combined Lagrange Multiplier Approach Preserving Original Energy Law for Dissipative Systems
Zhengguang Liu, Nan Zheng and Xiaoli LiInternational Journal for Numerical Methods in Engineering 126 (1) (2025)
https://doi.org/10.1002/nme.7619
Mathematical modeling and numerical simulation of the N-component Cahn-Hilliard model on evolving surfaces
Lulu Liu, Shijie Huang, Xufeng Xiao and Xinlong FengJournal of Computational Physics 513 113189 (2024)
https://doi.org/10.1016/j.jcp.2024.113189
A new phase field method for the simulation of wetting on rough surfaces
Yi ShiDiscrete and Continuous Dynamical Systems - B 29 (4) 1972 (2024)
https://doi.org/10.3934/dcdsb.2023163
Stability and error estimates of Strang splitting method for the nonlocal ternary conservative Allen–Cahn model
Zhifeng Weng, Shuying Zhai, Weizhong Dai, Yanfang Yang and Yuchang MoJournal of Computational and Applied Mathematics 441 115668 (2024)
https://doi.org/10.1016/j.cam.2023.115668
Energy dissipation and maximum bound principle preserving scheme for solving a nonlocal ternary Allen-Cahn model
Shuying Zhai, Zhifeng Weng, Yuchang Mo and Xinlong FengComputers & Mathematics with Applications 155 150 (2024)
https://doi.org/10.1016/j.camwa.2023.12.006
Fast and stable dimension splitting simulations for the hydrodynamically coupled three-component conserved Allen–Cahn phase field model
Yuna Yang, Yan Wang, Xufeng Xiao and Xinlong FengInternational Journal of Multiphase Flow 174 104765 (2024)
https://doi.org/10.1016/j.ijmultiphaseflow.2024.104765
Thermodynamically consistent hybrid computational models for fluid-particle interactions
Qi Hong and Qi WangJournal of Computational Physics 513 113147 (2024)
https://doi.org/10.1016/j.jcp.2024.113147
A modified phase field method for the simulation of two-phase system in complex geometries
Yi ShiPhysics of Fluids 36 (8) (2024)
https://doi.org/10.1063/5.0220227
IMEX methods for thin-film equations and Cahn–Hilliard equations with variable mobility
Saulo Orizaga and Thomas WitelskiComputational Materials Science 243 113145 (2024)
https://doi.org/10.1016/j.commatsci.2024.113145
EFFICIENT AND STABLE TIME INTEGRATION OF THE CAHN-HILLARD EQUATIONS: EXPLICIT, IMPLICIT, AND EXPLICIT-ITERATIVE SCHEMES
M. A Botchev, I. A Fakhurdinov and E. B SavenkovŽurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki 64 (8) 1366 (2024)
https://doi.org/10.31857/S0044466924080034
A numerical study of interface dynamics in fluid materials
Hairch Youssef, Abderrahmane Elmelouky, Mohamed Louzazni, Fouad Belhora and Mohamed MonkadeMatériaux & Techniques 112 (4) 401 (2024)
https://doi.org/10.1051/mattech/2024018
Efficient and Stable Time Integration of Cahn–Hilliard Equations: Explicit, Implicit, and Explicit Iterative Schemes
M. A. Botchev, I. A. Fahurdinov and E. B. SavenkovComputational Mathematics and Mathematical Physics 64 (8) 1726 (2024)
https://doi.org/10.1134/S0965542524700945
Three-dimensional lattice Boltzmann flux solver for three-phase/component flow
Da Zhang, Yan Li, Liang Gong, Chenlin Zhu and Chang ShuPhysics of Fluids 36 (8) (2024)
https://doi.org/10.1063/5.0224828
A decoupled finite element scheme for simulating the dynamics of red blood cells in an L-shaped cavity
Murad Ali Shah, Kejia Pan, Rui Chen, Zhengru Zhang and Dongdong HeComputers & Mathematics with Applications 140 169 (2023)
https://doi.org/10.1016/j.camwa.2023.04.005
2D/3D Fully Decoupled, Unconditionally Energy Stable Rotational Velocity Projection Method for Incompressible MHD System
Ke Zhang, Haiyan Su and Demin LiuJournal of Mathematical Fluid Mechanics 25 (4) (2023)
https://doi.org/10.1007/s00021-023-00823-6
High-order supplementary variable methods for thermodynamically consistent partial differential equations
Qi Hong, Qi Wang and Yuezheng GongComputer Methods in Applied Mechanics and Engineering 416 116306 (2023)
https://doi.org/10.1016/j.cma.2023.116306
Fully discrete, decoupled and energy-stable Fourier-Spectral numerical scheme for the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy flow regime of two-phase incompressible flows
Shilin Zeng, Ziqing Xie, Xiaofeng Yang and Jiangxing WangComputer Methods in Applied Mechanics and Engineering 415 116289 (2023)
https://doi.org/10.1016/j.cma.2023.116289
An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media
Jisheng Kou, Huangxin Chen, ShiGui Du and Shuyu SunInternational Journal for Numerical Methods in Engineering 124 (3) 546 (2023)
https://doi.org/10.1002/nme.7131
A highly efficient semi-implicit corrective SPH scheme for 2D/3D tumor growth model
Jinjing Huang, Yang Xu, Jingjun Zhao and Tao JiangEngineering Analysis with Boundary Elements 155 839 (2023)
https://doi.org/10.1016/j.enganabound.2023.07.010
An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen–Cahn fluids
Zhijun Tan, Junxiang Yang, Jianjun Chen and Junseok KimApplied Mathematics and Computation 438 127599 (2023)
https://doi.org/10.1016/j.amc.2022.127599
Numerical Approximations of Diblock Copolymer Model Using a Modified Leapfrog Time-Marching Scheme
Lizhen Chen, Ying Ma, Bo Ren and Guohui ZhangComputation 11 (11) 215 (2023)
https://doi.org/10.3390/computation11110215
Gradient Flows for Coupling Order Parameters and Mechanics
Leonie Schmeller and Dirk PeschkaSIAM Journal on Applied Mathematics 83 (1) 225 (2023)
https://doi.org/10.1137/22M148478X
Thermodynamically consistent hydrodynamic phase-field computational modeling for fluid-structure interaction with moving contact lines
Qi Hong, Yuezheng Gong and Jia ZhaoJournal of Computational Physics 492 112409 (2023)
https://doi.org/10.1016/j.jcp.2023.112409
Efficient linear, fully-decoupled and energy stable numerical scheme for a variable density and viscosity, volume-conserved, hydrodynamically coupled phase-field elastic bending energy model of lipid vesicles
Xiaofeng YangComputer Methods in Applied Mechanics and Engineering 400 115479 (2022)
https://doi.org/10.1016/j.cma.2022.115479
Energy-stable method for the Cahn–Hilliard equation in arbitrary domains
Junxiang Yang, Jian Wang and Junseok KimInternational Journal of Mechanical Sciences 228 107489 (2022)
https://doi.org/10.1016/j.ijmecsci.2022.107489
Error analysis of a decoupled, linear and stable finite element method for Cahn–Hilliard–Navier–Stokes equations
Yaoyao Chen, Yunqing Huang and Nianyu YiApplied Mathematics and Computation 421 126928 (2022)
https://doi.org/10.1016/j.amc.2022.126928
Highly efficient and unconditionally energy stable semi-discrete time-marching numerical scheme for the two-phase incompressible flow phase-field system with variable-density and viscosity
Chuanjun Chen and Xiaofeng YangScience China Mathematics 65 (12) 2631 (2022)
https://doi.org/10.1007/s11425-021-1932-x
Optimal rate convergence analysis of a numerical scheme for the ternary Cahn–Hilliard system with a Flory–Huggins–deGennes energy potential
Lixiu Dong, Cheng Wang, Steven M. Wise and Zhengru ZhangJournal of Computational and Applied Mathematics 415 114474 (2022)
https://doi.org/10.1016/j.cam.2022.114474
A fully-discrete decoupled finite element method for the conserved Allen–Cahn type phase-field model of three-phase fluid flow system
Xiaofeng Yang and Xiaoming HeComputer Methods in Applied Mechanics and Engineering 389 114376 (2022)
https://doi.org/10.1016/j.cma.2021.114376
An energy stable linear numerical method for thermodynamically consistent modeling of two-phase incompressible flow in porous media
Jisheng Kou, Xiuhua Wang, Shigui Du and Shuyu SunJournal of Computational Physics 451 110854 (2022)
https://doi.org/10.1016/j.jcp.2021.110854
A wettability pattern-mediated trapped bubble removal from a horizontal liquid–liquid interface
Imdad Uddin Chowdhury, Pallab Sinha Mahapatra and Ashis Kumar SenPhysics of Fluids 34 (4) (2022)
https://doi.org/10.1063/5.0086149
A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model
Yuzhe Qin, Rui Chen and Zhengru ZhangMathematical Methods in the Applied Sciences 45 (5) 2776 (2022)
https://doi.org/10.1002/mma.7952
High-order discontinuous Galerkin approximation for a three-phase incompressible Navier–Stokes/Cahn–Hilliard model
Juan Manzanero, Carlos Redondo, Miguel Chávez-Módena, Gonzalo Rubio, Eusebio Valero, Susana Gómez-Álvarez and Ángel Rivero-JiménezComputers & Fluids 244 105545 (2022)
https://doi.org/10.1016/j.compfluid.2022.105545
Nonlocal operator method for the Cahn-Hilliard phase field model
Huilong Ren, Xiaoying Zhuang, Nguyen-Thoi Trung and Timon RabczukCommunications in Nonlinear Science and Numerical Simulation 96 105687 (2021)
https://doi.org/10.1016/j.cnsns.2020.105687
Efficient, second-order in time, and energy stable scheme for a new hydrodynamically coupled three components volume-conserved Allen–Cahn phase-field model
Xiaofeng YangMathematical Models and Methods in Applied Sciences 31 (04) 753 (2021)
https://doi.org/10.1142/S0218202521500184
A new efficient fully-decoupled and second-order time-accurate scheme for Cahn–Hilliard phase-field model of three-phase incompressible flow
Xiaofeng YangComputer Methods in Applied Mechanics and Engineering 376 113589 (2021)
https://doi.org/10.1016/j.cma.2020.113589
Linear energy stable and maximum principle preserving semi-implicit scheme for Allen–Cahn equation with double well potential
Xiuhua Wang, Jisheng Kou and Huicai GaoCommunications in Nonlinear Science and Numerical Simulation 98 105766 (2021)
https://doi.org/10.1016/j.cnsns.2021.105766
Efficient and energy stable scheme for the hydrodynamically coupled three components Cahn-Hilliard phase-field model using the stabilized-Invariant Energy Quadratization (S-IEQ) Approach
Xiaofeng YangJournal of Computational Physics 438 110342 (2021)
https://doi.org/10.1016/j.jcp.2021.110342
Numerical approximations of the Navier–Stokes equation coupled with volume-conserved multi-phase-field vesicles system: Fully-decoupled, linear, unconditionally energy stable and second-order time-accurate numerical scheme
Xiaofeng YangComputer Methods in Applied Mechanics and Engineering 375 113600 (2021)
https://doi.org/10.1016/j.cma.2020.113600
Phase-field modeling of wetting and balling dynamics in powder bed fusion process
Lu Li, Ji-Qin Li and Tai-Hsi FanPhysics of Fluids 33 (4) (2021)
https://doi.org/10.1063/5.0046771
Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model
Guo-Dong Zhang, Xiaoming He and Xiaofeng YangSIAM Journal on Scientific Computing 43 (1) B167 (2021)
https://doi.org/10.1137/19M1288280
Numerical study of the ternary Cahn–Hilliard fluids by using an efficient modified scalar auxiliary variable approach
Junxiang Yang and Junseok KimCommunications in Nonlinear Science and Numerical Simulation 102 105923 (2021)
https://doi.org/10.1016/j.cnsns.2021.105923
A discontinuous Galerkin approximation for a wall–bounded consistent three–component Cahn–Hilliard flow model
Juan Manzanero, Carlos Redondo, Gonzalo Rubio, Esteban Ferrer and Ángel Rivero–JiménezComputers & Fluids 225 104971 (2021)
https://doi.org/10.1016/j.compfluid.2021.104971
New efficient time-stepping schemes for the Navier–Stokes–Cahn–Hilliard equations
Minghui Li and Chuanju XuComputers & Fluids 231 105174 (2021)
https://doi.org/10.1016/j.compfluid.2021.105174
Fully-discrete finite element numerical scheme with decoupling structure and energy stability for the Cahn–Hilliard phase-field model of two-phase incompressible flow system with variable density and viscosity
Chuanjun Chen and Xiaofeng YangESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2323 (2021)
https://doi.org/10.1051/m2an/2021056
A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters
Lixiu Dong, Cheng Wang, Steven M. Wise and Zhengru ZhangJournal of Computational Physics 442 110451 (2021)
https://doi.org/10.1016/j.jcp.2021.110451
A conservative level set method for N-phase flows with a free-energy-based surface tension model
Amanda A. Howard and Alexandre M. TartakovskyJournal of Computational Physics 426 109955 (2021)
https://doi.org/10.1016/j.jcp.2020.109955
Long time Hαs stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity
Wansheng Wang, Zheng Wang and Zhaoxiang LiApplied Numerical Mathematics 165 35 (2021)
https://doi.org/10.1016/j.apnum.2021.02.005
Generalized SAV approaches for gradient systems
Qing Cheng, Chun Liu and Jie ShenJournal of Computational and Applied Mathematics 394 113532 (2021)
https://doi.org/10.1016/j.cam.2021.113532
An Energy Stable Finite Element Scheme for the Three-Component Cahn–Hilliard-Type Model for Macromolecular Microsphere Composite Hydrogels
Maoqin Yuan, Wenbin Chen, Cheng Wang, Steven M. Wise and Zhengru ZhangJournal of Scientific Computing 87 (3) (2021)
https://doi.org/10.1007/s10915-021-01508-w
Phase-field modeling of selective laser brazing of diamond grits
Lu Li, Shuai Li, Bi Zhang and Tai-Hsi FanPhysics of Fluids 33 (5) (2021)
https://doi.org/10.1063/5.0049096
Error Analysis of a Decoupled, Linear Stabilization Scheme for the Cahn–Hilliard Model of Two-Phase Incompressible Flows
Zhen Xu, Xiaofeng Yang and Hui ZhangJournal of Scientific Computing 83 (3) (2020)
https://doi.org/10.1007/s10915-020-01241-w
Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential
Xiuhua Wang, Jisheng Kou and Jianchao CaiJournal of Scientific Computing 82 (2) (2020)
https://doi.org/10.1007/s10915-020-01127-x
Energy Stable Numerical Schemes for Ternary Cahn-Hilliard System
Wenbin Chen, Cheng Wang, Shufen Wang, Xiaoming Wang and Steven M. WiseJournal of Scientific Computing 84 (2) (2020)
https://doi.org/10.1007/s10915-020-01276-z
Contrasting phase field method and pairwise force smoothed particle hydrodynamics method in simulating multiphase flow through fracture-vug medium
Wei Yang, Junsheng Zeng and Dongxiao ZhangJournal of Natural Gas Science and Engineering 81 103424 (2020)
https://doi.org/10.1016/j.jngse.2020.103424
A phase field method for the numerical simulation of rigid particulate in two-phase flows
Shi YiFluid Dynamics Research 52 (1) 015512 (2020)
https://doi.org/10.1088/1873-7005/ab6aac
Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations
Guo-Dong Zhang, Xiaoming He and Xiaofeng YangJournal of Computational and Applied Mathematics 369 112636 (2020)
https://doi.org/10.1016/j.cam.2019.112636
Unconditionally energy stable large time stepping method for the L2-gradient flow based ternary phase-field model with precise nonlocal volume conservation
Jun Zhang and Xiaofeng YangComputer Methods in Applied Mechanics and Engineering 361 112743 (2020)
https://doi.org/10.1016/j.cma.2019.112743
Decoupled, non-iterative, and unconditionally energy stable large time stepping method for the three-phase Cahn-Hilliard phase-field model
Jun Zhang and Xiaofeng YangJournal of Computational Physics 404 109115 (2020)
https://doi.org/10.1016/j.jcp.2019.109115
Multi-component chemo-mechanics based on transport relations for the chemical potential
P. Shanthraj, C. Liu, A. Akbarian, B. Svendsen and D. RaabeComputer Methods in Applied Mechanics and Engineering 365 113029 (2020)
https://doi.org/10.1016/j.cma.2020.113029
Efficient linear schemes for the nonlocal Cahn–Hilliard equation of phase field models
Xiaofeng Yang and Jia ZhaoComputer Physics Communications 235 234 (2019)
https://doi.org/10.1016/j.cpc.2018.08.012
Efficient energy-stable schemes for the hydrodynamics coupled phase-field model
Guangpu Zhu, Huangxin Chen, Jun Yao and Shuyu SunApplied Mathematical Modelling 70 82 (2019)
https://doi.org/10.1016/j.apm.2018.12.017
An unconditionally energy-stable scheme based on an implicit auxiliary energy variable for incompressible two-phase flows with different densities involving only precomputable coefficient matrices
Zhiguo Yang and Suchuan DongJournal of Computational Physics 393 229 (2019)
https://doi.org/10.1016/j.jcp.2019.05.018
A linear, second-order, energy stable, fully adaptive finite element method for phase-field modelling of wetting phenomena
Benjamin Aymard, Urbain Vaes, Marc Pradas and Serafim KalliadasisJournal of Computational Physics: X 2 100010 (2019)
https://doi.org/10.1016/j.jcpx.2019.100010
Simulation of the phase field Cahn–Hilliard and tumor growth models via a numerical scheme: Element-free Galerkin method
Vahid Mohammadi and Mehdi DehghanComputer Methods in Applied Mechanics and Engineering 345 919 (2019)
https://doi.org/10.1016/j.cma.2018.11.019
WITHDRAWN: A linear, second-order, energy stable, fully adaptive finite-element method for phase-field modelling of wetting phenomena
Benjamin Aymard, Urbain Vaes, Marc Pradas and Serafim KalliadasisJournal of Computational Physics (2018)
https://doi.org/10.1016/j.jcp.2018.11.036
A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging
Florian Frank, Chen Liu, Faruk O. Alpak and Beatrice RiviereComputational Geosciences 22 (2) 543 (2018)
https://doi.org/10.1007/s10596-017-9709-1
Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
Xiaofeng Yang, Jia Zhao, Qi Wang and Jie ShenMathematical Models and Methods in Applied Sciences 27 (11) 1993 (2017)
https://doi.org/10.1142/S0218202517500373
The Cahn–Hilliard equation and some of its variants
Alain MiranvilleAIMS Mathematics 2 (3) 479 (2017)
https://doi.org/10.3934/Math.2017.2.479
Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow
Jia Zhao, Huiyuan Li, Qi Wang and Xiaofeng YangJournal of Scientific Computing 70 (3) 1367 (2017)
https://doi.org/10.1007/s10915-016-0283-9
Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines
Lina Ma, Rui Chen, Xiaofeng Yang and Hui ZhangCommunications in Computational Physics 21 (3) 867 (2017)
https://doi.org/10.4208/cicp.OA-2016-0008
Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow
L’ubomír Baňas and Robert NürnbergESAIM: Mathematical Modelling and Numerical Analysis 51 (3) 1089 (2017)
https://doi.org/10.1051/m2an/2016048
Remarks on continuum theory of mixtures: editorial to special issue on mixture theory
K. V. Mohankumar, Vít Průša, K. Kannan and A. S. WinemanInternational Journal of Advances in Engineering Sciences and Applied Mathematics 9 (2) 120 (2017)
https://doi.org/10.1007/s12572-017-0185-6
Wall-bounded multiphase flows of N immiscible incompressible fluids: Consistency and contact-angle boundary condition
S. DongJournal of Computational Physics 338 21 (2017)
https://doi.org/10.1016/j.jcp.2017.02.048
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model
Qing Cheng, Xiaofeng Yang and Jie ShenJournal of Computational Physics 341 44 (2017)
https://doi.org/10.1016/j.jcp.2017.04.010
A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions
Franck Boyer and Flore NabetESAIM: Mathematical Modelling and Numerical Analysis 51 (5) 1691 (2017)
https://doi.org/10.1051/m2an/2016073
Multiphase Allen–Cahn and Cahn–Hilliard models and their discretizations with the effect of pairwise surface tensions
Shuonan Wu and Jinchao XuJournal of Computational Physics 343 10 (2017)
https://doi.org/10.1016/j.jcp.2017.04.039
On some practical issues concerning the implementation of Cahn–Hilliard–Navier–Stokes type models
Martin Řehoř, Jan Blechta and Ondřej SoučekInternational Journal of Advances in Engineering Sciences and Applied Mathematics 9 (1) 30 (2017)
https://doi.org/10.1007/s12572-016-0171-4
A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State
Xiaolin Fan, Jisheng Kou, Zhonghua Qiao and Shuyu SunSIAM Journal on Scientific Computing 39 (1) B1 (2017)
https://doi.org/10.1137/16M1061552
Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model
Xiaofeng Yang and Lili JuComputer Methods in Applied Mechanics and Engineering 318 1005 (2017)
https://doi.org/10.1016/j.cma.2017.02.011
Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model
Mehdi Dehghan and Vahid MohammadiCommunications in Nonlinear Science and Numerical Simulation 44 204 (2017)
https://doi.org/10.1016/j.cnsns.2016.07.024
Diffuse interface simulation of ternary fluids in contact with solid
Chun-Yu Zhang, Hang Ding, Peng Gao and Yan-Ling WuJournal of Computational Physics 309 37 (2016)
https://doi.org/10.1016/j.jcp.2015.12.054
A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids
Jia Zhao, Xiaofeng Yang, Jie Shen and Qi WangJournal of Computational Physics 305 539 (2016)
https://doi.org/10.1016/j.jcp.2015.09.044
A practical numerical scheme for the ternary Cahn–Hilliard system with a logarithmic free energy
Darae Jeong and Junseok KimPhysica A: Statistical Mechanics and its Applications 442 510 (2016)
https://doi.org/10.1016/j.physa.2015.09.038
Convergence of a finite-volume scheme for the Cahn–Hilliard equation with dynamic boundary conditions
Flore NabetIMA Journal of Numerical Analysis 36 (4) 1898 (2016)
https://doi.org/10.1093/imanum/drv057
Numerical approximations to a new phase field model for two phase flows of complex fluids
Jia Zhao, Qi Wang and Xiaofeng YangComputer Methods in Applied Mechanics and Engineering 310 77 (2016)
https://doi.org/10.1016/j.cma.2016.06.008
Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition
K. Sagiyama, S. Rudraraju and K. GarikipatiComputer Methods in Applied Mechanics and Engineering 311 556 (2016)
https://doi.org/10.1016/j.cma.2016.09.003
A Decoupled Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Hele-Shaw System
Daozhi HanJournal of Scientific Computing 66 (3) 1102 (2016)
https://doi.org/10.1007/s10915-015-0055-y
Unconditionally energy stable time stepping scheme for Cahn–Morral equation: Application to multi-component spinodal decomposition and optimal space tiling
Rouhollah TavakoliJournal of Computational Physics 304 441 (2016)
https://doi.org/10.1016/j.jcp.2015.10.018
Improving the accuracy of convexity splitting methods for gradient flow equations
Karl Glasner and Saulo OrizagaJournal of Computational Physics 315 52 (2016)
https://doi.org/10.1016/j.jcp.2016.03.042
Numerical Methods for Solving the Cahn–Hilliard Equation and Its Applicability to Related Energy-Based Models
G. Tierra and F. Guillén-GonzálezArchives of Computational Methods in Engineering 22 (2) 269 (2015)
https://doi.org/10.1007/s11831-014-9112-1
Decoupled energy stable schemes for phase-field vesicle membrane model
Rui Chen, Guanghua Ji, Xiaofeng Yang and Hui ZhangJournal of Computational Physics 302 509 (2015)
https://doi.org/10.1016/j.jcp.2015.09.025
Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows
Jie Shen and Xiaofeng YangSIAM Journal on Numerical Analysis 53 (1) 279 (2015)
https://doi.org/10.1137/140971154
An efficient numerical method for simulating multiphase flows using a diffuse interface model
Hyun Geun Lee and Junseok KimPhysica A: Statistical Mechanics and its Applications 423 33 (2015)
https://doi.org/10.1016/j.physa.2014.12.027
Physical formulation and numerical algorithm for simulating N immiscible incompressible fluids involving general order parameters
S. DongJournal of Computational Physics 283 98 (2015)
https://doi.org/10.1016/j.jcp.2014.11.039
Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids
Jie Shen and Xiaofeng YangSIAM Journal on Scientific Computing 36 (1) B122 (2014)
https://doi.org/10.1137/130921593
Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects
Flore NabetSpringer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects 77 401 (2014)
https://doi.org/10.1007/978-3-319-05684-5_39