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:
Franck Boyer, Sebastian Minjeaud
ESAIM: M2AN, 45 4 (2011) 697-738
Published online: 2010-12-10
This article has been cited by the following article(s):
Efficient numerical solution of discrete multi-component Cahn–Hilliard systems
P. Boyanova and M. Neytcheva
Computers & Mathematics with Applications 67 (1) 106 (2014)
DOI: 10.1016/j.camwa.2013.10.013
See this article
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 Zhang
Journal of Computational Physics 442 110451 (2021)
DOI: 10.1016/j.jcp.2021.110451
See this article
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 Yang
Computer Methods in Applied Mechanics and Engineering 400 115479 (2022)
DOI: 10.1016/j.cma.2022.115479
See this article
Flore Nabet
77 401 (2014)
DOI: 10.1007/978-3-319-05684-5_39
See this article
The Cahn–Hilliard equation and some of its variants
Alain Miranville
AIMS Mathematics 2 (3) 479 (2017)
DOI: 10.3934/Math.2017.2.479
See this article
An efficient algorithm for incompressible N-phase flows
S. Dong
Journal of Computational Physics 276 691 (2014)
DOI: 10.1016/j.jcp.2014.08.002
See this article
The Cahn-Hilliard Equation with Logarithmic Potentials
Laurence Cherfils, Alain Miranville and Sergey Zelik
Milan Journal of Mathematics 79 (2) 561 (2011)
DOI: 10.1007/s00032-011-0165-4
See this article
Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids
Jie Shen and Xiaofeng Yang
SIAM Journal on Scientific Computing 36 (1) B122 (2014)
DOI: 10.1137/130921593
See this article
On some practical issues concerning the implementation of Cahn–Hilliard–Navier–Stokes type models
Martin Řehoř, Jan Blechta and Ondřej Souček
International Journal of Advances in Engineering Sciences and Applied Mathematics 9 (1) 30 (2017)
DOI: 10.1007/s12572-016-0171-4
See this article
Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow
L’ubomír Baňas and Robert Nürnberg
ESAIM: Mathematical Modelling and Numerical Analysis 51 (3) 1089 (2017)
DOI: 10.1051/m2an/2016048
See this article
Simulation of sharp interface multi-material flows involving an arbitrary number of components through an extended five-equation model
Marie Billaud Friess and Samuel Kokh
Journal of Computational Physics 273 488 (2014)
DOI: 10.1016/j.jcp.2014.05.012
See this article
Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models
X. Wu, G. J. van Zwieten and K. G. van der Zee
International Journal for Numerical Methods in Biomedical Engineering 30 (2) 180 (2014)
DOI: 10.1002/cnm.2597
See this article
Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows
Jie Shen and Xiaofeng Yang
SIAM Journal on Numerical Analysis 53 (1) 279 (2015)
DOI: 10.1137/140971154
See this article
A practical numerical scheme for the ternary Cahn–Hilliard system with a logarithmic free energy
Darae Jeong and Junseok Kim
Physica A: Statistical Mechanics and its Applications 442 510 (2016)
DOI: 10.1016/j.physa.2015.09.038
See this article
Modeling and simulation of dynamics of three-component flows on solid surface
Yi Shi and Xiao-Ping Wang
Japan Journal of Industrial and Applied Mathematics 31 (3) 611 (2014)
DOI: 10.1007/s13160-014-0151-7
See this article
An unconditionally stable uncoupled scheme for a triphasic Cahn-Hilliard/Navier-Stokes model
Sebastian Minjeaud
Numerical Methods for Partial Differential Equations 29 (2) 584 (2013)
DOI: 10.1002/num.21721
See this article
Numerical Methods for Solving the Cahn–Hilliard Equation and Its Applicability to Related Energy-Based Models
G. Tierra and F. Guillén-González
Archives of Computational Methods in Engineering 22 (2) 269 (2015)
DOI: 10.1007/s11831-014-9112-1
See this article
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 Riviere
Computational Geosciences 22 (2) 543 (2018)
DOI: 10.1007/s10596-017-9709-1
See this article
Numerical approximations to a new phase field model for two phase flows of complex fluids
Jia Zhao, Qi Wang and Xiaofeng Yang
Computer Methods in Applied Mechanics and Engineering 310 77 (2016)
DOI: 10.1016/j.cma.2016.06.008
See this article
On linear schemes for a Cahn–Hilliard diffuse interface model
F. Guillén-González and G. Tierra
Journal of Computational Physics 234 140 (2013)
DOI: 10.1016/j.jcp.2012.09.020
See this article
Energy Stable Numerical Schemes for Ternary Cahn-Hilliard System
Wenbin Chen, Cheng Wang, Shufen Wang, Xiaoming Wang and Steven M. Wise
Journal of Scientific Computing 84 (2) (2020)
DOI: 10.1007/s10915-020-01276-z
See this article
A Decoupled Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Hele-Shaw System
Daozhi Han
Journal of Scientific Computing 66 (3) 1102 (2016)
DOI: 10.1007/s10915-015-0055-y
See this article
A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions
Franck Boyer and Flore Nabet
ESAIM: Mathematical Modelling and Numerical Analysis 51 (5) 1691 (2017)
DOI: 10.1051/m2an/2016073
See this article
Physical formulation and numerical algorithm for simulating N immiscible incompressible fluids involving general order parameters
S. Dong
Journal of Computational Physics 283 98 (2015)
DOI: 10.1016/j.jcp.2014.11.039
See this article
Hierarchy of consistent n-component Cahn–Hilliard systems
Franck Boyer and Sebastian Minjeaud
Mathematical Models and Methods in Applied Sciences 24 (14) 2885 (2014)
DOI: 10.1142/S0218202514500407
See this article
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 Shen
Mathematical Models and Methods in Applied Sciences 27 (11) 1993 (2017)
DOI: 10.1142/S0218202517500373
See this article
Convergence of a finite-volume scheme for the Cahn–Hilliard equation with dynamic boundary conditions
Flore Nabet
IMA Journal of Numerical Analysis 36 (4) 1898 (2016)
DOI: 10.1093/imanum/drv057
See this article
Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow
Jia Zhao, Huiyuan Li, Qi Wang and Xiaofeng Yang
Journal of Scientific Computing 70 (3) 1367 (2017)
DOI: 10.1007/s10915-016-0283-9
See this article
Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model
Mehdi Dehghan and Vahid Mohammadi
Communications in Nonlinear Science and Numerical Simulation 44 204 (2017)
DOI: 10.1016/j.cnsns.2016.07.024
See this article
Unconditionally energy stable time stepping scheme for Cahn–Morral equation: Application to multi-component spinodal decomposition and optimal space tiling
Rouhollah Tavakoli
Journal of Computational Physics 304 441 (2016)
DOI: 10.1016/j.jcp.2015.10.018
See this article
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 Sun
SIAM Journal on Scientific Computing 39 (1) B1 (2017)
DOI: 10.1137/16M1061552
See this article
Remarks on continuum theory of mixtures: editorial to special issue on mixture theory
K. V. Mohankumar, Vít Průša, K. Kannan and A. S. Wineman
International Journal of Advances in Engineering Sciences and Applied Mathematics 9 (2) 120 (2017)
DOI: 10.1007/s12572-017-0185-6
See this article
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 Yang
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2323 (2021)
DOI: 10.1051/m2an/2021056
See this article
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 Dong
Journal of Computational Physics 393 229 (2019)
DOI: 10.1016/j.jcp.2019.05.018
See this article
Simulation of the phase field Cahn–Hilliard and tumor growth models via a numerical scheme: Element-free Galerkin method
Vahid Mohammadi and Mehdi Dehghan
Computer Methods in Applied Mechanics and Engineering 345 919 (2019)
DOI: 10.1016/j.cma.2018.11.019
See this article
Efficient energy-stable schemes for the hydrodynamics coupled phase-field model
Guangpu Zhu, Huangxin Chen, Jun Yao and Shuyu Sun
Applied Mathematical Modelling 70 82 (2019)
DOI: 10.1016/j.apm.2018.12.017
See this article
A linear, second-order, energy stable, fully adaptive finite-element method for phase-field modeling of wetting phenomena
Benjamin Aymard, Urbain Vaes, Marc Pradas and Serafim Kalliadasis
Journal of Computational Physics (2018)
DOI: 10.1016/j.jcp.2018.11.036
See this article
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 Kalliadasis
Journal of Computational Physics: X 2 100010 (2019)
DOI: 10.1016/j.jcpx.2019.100010
See this article
Diffuse interface simulation of ternary fluids in contact with solid
Chun-Yu Zhang, Hang Ding, Peng Gao and Yan-Ling Wu
Journal of Computational Physics 309 37 (2016)
DOI: 10.1016/j.jcp.2015.12.054
See this article
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 Zhang
Communications in Computational Physics 21 (3) 867 (2017)
DOI: 10.4208/cicp.OA-2016-0008
See this article
Efficient linear schemes for the nonlocal Cahn–Hilliard equation of phase field models
Xiaofeng Yang and Jia Zhao
Computer Physics Communications 235 234 (2019)
DOI: 10.1016/j.cpc.2018.08.012
See this article
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 Yang
Computer Methods in Applied Mechanics and Engineering 361 112743 (2020)
DOI: 10.1016/j.cma.2019.112743
See this article
A phase field method for the numerical simulation of rigid particulate in two-phase flows
Shi Yi
Fluid Dynamics Research 52 (1) 015512 (2020)
DOI: 10.1088/1873-7005/ab6aac
See this article
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model
Qing Cheng, Xiaofeng Yang and Jie Shen
Journal of Computational Physics 341 44 (2017)
DOI: 10.1016/j.jcp.2017.04.010
See this article
Multiphase Allen–Cahn and Cahn–Hilliard models and their discretizations with the effect of pairwise surface tensions
Shuonan Wu and Jinchao Xu
Journal of Computational Physics 343 10 (2017)
DOI: 10.1016/j.jcp.2017.04.039
See this article
Multi-component chemo-mechanics based on transport relations for the chemical potential
P. Shanthraj, C. Liu, A. Akbarian, B. Svendsen and D. Raabe
Computer Methods in Applied Mechanics and Engineering 365 113029 (2020)
DOI: 10.1016/j.cma.2020.113029
See this article
A conservative level set method for N-phase flows with a free-energy-based surface tension model
Amanda A. Howard and Alexandre M. Tartakovsky
Journal of Computational Physics 426 109955 (2021)
DOI: 10.1016/j.jcp.2020.109955
See this article
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 Zhang
Journal of Natural Gas Science and Engineering 81 103424 (2020)
DOI: 10.1016/j.jngse.2020.103424
See this article
Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential
Xiuhua Wang, Jisheng Kou and Jianchao Cai
Journal of Scientific Computing 82 (2) (2020)
DOI: 10.1007/s10915-020-01127-x
See this article
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 Yang
SIAM Journal on Scientific Computing 43 (1) B167 (2021)
DOI: 10.1137/19M1288280
See this article
Linear energy stable and maximum principle preserving semi-implicit scheme for Allen–Cahn equation with double well potential
Xiuhua Wang, Jisheng Kou and Huicai Gao
Communications in Nonlinear Science and Numerical Simulation 98 105766 (2021)
DOI: 10.1016/j.cnsns.2021.105766
See this article
Nonlocal operator method for the Cahn-Hilliard phase field model
Huilong Ren, Xiaoying Zhuang, Nguyen-Thoi Trung and Timon Rabczuk
Communications in Nonlinear Science and Numerical Simulation 96 105687 (2021)
DOI: 10.1016/j.cnsns.2020.105687
See this article
Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model
Xiaofeng Yang and Lili Ju
Computer Methods in Applied Mechanics and Engineering 318 1005 (2017)
DOI: 10.1016/j.cma.2017.02.011
See this article
Decoupled, non-iterative, and unconditionally energy stable large time stepping method for the three-phase Cahn-Hilliard phase-field model
Jun Zhang and Xiaofeng Yang
Journal of Computational Physics 404 109115 (2020)
DOI: 10.1016/j.jcp.2019.109115
See this article
Long time Hαs stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity
Wansheng Wang, Zheng Wang and Zhaoxiang Li
Applied Numerical Mathematics 165 35 (2021)
DOI: 10.1016/j.apnum.2021.02.005
See this article
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 Wang
Journal of Computational Physics 305 539 (2016)
DOI: 10.1016/j.jcp.2015.09.044
See this article
Improving the accuracy of convexity splitting methods for gradient flow equations
Karl Glasner and Saulo Orizaga
Journal of Computational Physics 315 52 (2016)
DOI: 10.1016/j.jcp.2016.03.042
See this article
Wall-bounded multiphase flows of N immiscible incompressible fluids: Consistency and contact-angle boundary condition
S. Dong
Journal of Computational Physics 338 21 (2017)
DOI: 10.1016/j.jcp.2017.02.048
See this article
Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition
K. Sagiyama, S. Rudraraju and K. Garikipati
Computer Methods in Applied Mechanics and Engineering 311 556 (2016)
DOI: 10.1016/j.cma.2016.09.003
See this article
Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations
Guo-Dong Zhang, Xiaoming He and Xiaofeng Yang
Journal of Computational and Applied Mathematics 369 112636 (2020)
DOI: 10.1016/j.cam.2019.112636
See this article
Phase-field modeling of wetting and balling dynamics in powder bed fusion process
Lu Li, Ji-Qin Li and Tai-Hsi Fan
Physics of Fluids 33 (4) 042116 (2021)
DOI: 10.1063/5.0046771
See this article
Generalized SAV approaches for gradient systems
Qing Cheng, Chun Liu and Jie Shen
Journal of Computational and Applied Mathematics 394 113532 (2021)
DOI: 10.1016/j.cam.2021.113532
See this article
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–Jiménez
Computers & Fluids 225 104971 (2021)
DOI: 10.1016/j.compfluid.2021.104971
See this article
Phase-field modeling of selective laser brazing of diamond grits
Lu Li, Shuai Li, Bi Zhang and Tai-Hsi Fan
Physics of Fluids 33 (5) 052113 (2021)
DOI: 10.1063/5.0049096
See this article
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 Zhang
Journal of Scientific Computing 87 (3) (2021)
DOI: 10.1007/s10915-021-01508-w
See this article
Error Analysis of a Decoupled, Linear Stabilization Scheme for the Cahn–Hilliard Model of Two-Phase Incompressible Flows
Zhen Xu, Xiaofeng Yang and Hui Zhang
Journal of Scientific Computing 83 (3) (2020)
DOI: 10.1007/s10915-020-01241-w
See this article
A new efficient fully-decoupled and second-order time-accurate scheme for Cahn–Hilliard phase-field model of three-phase incompressible flow
Xiaofeng Yang
Computer Methods in Applied Mechanics and Engineering 376 113589 (2021)
DOI: 10.1016/j.cma.2020.113589
See this article
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 Yang
Computer Methods in Applied Mechanics and Engineering 375 113600 (2021)
DOI: 10.1016/j.cma.2020.113600
See this article
New efficient time-stepping schemes for the Navier–Stokes–Cahn–Hilliard equations
Minghui Li and Chuanju Xu
Computers & Fluids 231 105174 (2021)
DOI: 10.1016/j.compfluid.2021.105174
See this article
A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model
Yuzhe Qin, Rui Chen and Zhengru Zhang
Mathematical Methods in the Applied Sciences 45 (5) 2776 (2022)
DOI: 10.1002/mma.7952
See this article
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 He
Computer Methods in Applied Mechanics and Engineering 389 114376 (2022)
DOI: 10.1016/j.cma.2021.114376
See this article
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 Sun
Journal of Computational Physics 451 110854 (2022)
DOI: 10.1016/j.jcp.2021.110854
See this article
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 Yang
Journal of Computational Physics 438 110342 (2021)
DOI: 10.1016/j.jcp.2021.110342
See this article
Error analysis of a decoupled, linear and stable finite element method for Cahn–Hilliard–Navier–Stokes equations
Yaoyao Chen, Yunqing Huang and Nianyu Yi
Applied Mathematics and Computation 421 126928 (2022)
DOI: 10.1016/j.amc.2022.126928
See this article
Gradient Flows for Coupling Order Parameters and Mechanics
Leonie Schmeller and Dirk Peschka
SIAM Journal on Applied Mathematics 83 (1) 225 (2023)
DOI: 10.1137/22M148478X
See this article
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 Yang
Science China Mathematics 65 (12) 2631 (2022)
DOI: 10.1007/s11425-021-1932-x
See this article
A wettability pattern-mediated trapped bubble removal from a horizontal liquid–liquid interface
Imdad Uddin Chowdhury, Pallab Sinha Mahapatra and Ashis Kumar Sen
Physics of Fluids 34 (4) 042109 (2022)
DOI: 10.1063/5.0086149
See this article
Decoupled energy stable schemes for phase-field vesicle membrane model
Rui Chen, Guanghua Ji, Xiaofeng Yang and Hui Zhang
Journal of Computational Physics 302 509 (2015)
DOI: 10.1016/j.jcp.2015.09.025
See this article
Energy-stable method for the Cahn–Hilliard equation in arbitrary domains
Junxiang Yang, Jian Wang and Junseok Kim
International Journal of Mechanical Sciences 228 107489 (2022)
DOI: 10.1016/j.ijmecsci.2022.107489
See this article
An efficient numerical method for simulating multiphase flows using a diffuse interface model
Hyun Geun Lee and Junseok Kim
Physica A: Statistical Mechanics and its Applications 423 33 (2015)
DOI: 10.1016/j.physa.2014.12.027
See this article
Buoyancy-driven mixing of multi-component fluids in two-dimensional tilted channels
Hyun Geun Lee and Junseok Kim
European Journal of Mechanics - B/Fluids 42 37 (2013)
DOI: 10.1016/j.euromechflu.2013.06.004
See this article
Numerical study of the ternary Cahn–Hilliard fluids by using an efficient modified scalar auxiliary variable approach
Junxiang Yang and Junseok Kim
Communications in Nonlinear Science and Numerical Simulation 102 105923 (2021)
DOI: 10.1016/j.cnsns.2021.105923
See this article
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-Jiménez
Computers & Fluids 244 105545 (2022)
DOI: 10.1016/j.compfluid.2022.105545
See this article
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 Sun
International Journal for Numerical Methods in Engineering 124 (3) 546 (2023)
DOI: 10.1002/nme.7131
See this article
An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen–Cahn fluids
Zhijun Tan, Junxiang Yang, Jianjun Chen and Junseok Kim
Applied Mathematics and Computation 438 127599 (2023)
DOI: 10.1016/j.amc.2022.127599
See this article
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 Zhang
Journal of Computational and Applied Mathematics 415 114474 (2022)
DOI: 10.1016/j.cam.2022.114474
See this article