-
Previous Article
Three steps on an open road
- IPI Home
- This Issue
-
Next Article
A texture model based on a concentration of measure
3D adaptive finite element method for a phase field model for the moving contact line problems
1. | Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China |
2. | Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia |
3. | Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong |
References:
[1] |
H. D. Ceniceros, Rudimar L. Nos and Alexandre M. Roma, Theree-dimensional, fully adaptive simulations of phase-field fluid models, J. Comput. Phys., 229 (2010), 6135-6155.
doi: 10.1016/j.jcp.2010.04.045. |
[2] |
Qingming Chang and J. I. D. Alexander, Analysis of single droplet dynamics on striped surface domains using a lattice Boltzmann method, Microfluid Nanofluid, 2 (2006), 309-326.
doi: 10.1007/s10404-005-0075-2. |
[3] |
Yana Di, Ruo Li and Tao Tang, A general moving mesh framework in 3D and its application for simulating the mixture of multi-phase flows, Commun. Comput. Phys., 3 (2008), 582-602. |
[4] |
Yana Di and Xiao-Ping Wang, Precursor simulations in spreading using a multi-mesh adaptive finite elment method, J. Comput. Phys., 228 (2009), 1380-1390.
doi: 10.1016/j.jcp.2008.10.028. |
[5] |
Q. Du and R. A. Nicolaides, Numerical analysis of a continuum model of phase transition, SIAM J. Numer. Anal., 28 (1991), 1310-1322.
doi: 10.1137/0728069. |
[6] |
Qiang Du and Jian Zhang, Adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations, SIAM J. Sci. Comput., 30 (2008), 1634-1657.
doi: 10.1137/060656449. |
[7] |
A. Dupuis and J. M. Yeomans, Droplet dynamics on patterned substrates, Pramana J. Phys., 64 (2005), 1019-1027.
doi: 10.1007/BF02704164. |
[8] |
Xiaobing Feng, Fully discrete finite element approximations of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two phase flows, SIAM J. Numer. Anal., 44 (2006), 1049-1072.
doi: 10.1137/050638333. |
[9] |
Xiaobing Feng and A. Prohl, Error analysis of a mixed finite element method for the Cahn-Hilliard equation, Numer. Math., 99 (2004), 47-84.
doi: 10.1007/s00211-004-0546-5. |
[10] |
Min Gao and Xiao-Ping Wang, A gradient stable scheme for a phase field model for the moving contact line problem, J. Comput. Phys., 231 (2012), 1372-1386.
doi: 10.1016/j.jcp.2011.10.015. |
[11] |
V. Girault and P.-A. Raviart, "Finite Element Method for Navier-Stokes Equations. Theory and Algorithms," Springer Series in Computational Mathematics, 5, Springer-Verlag, Berlin, 1986.
doi: 10.1007/978-3-642-61623-5. |
[12] |
Qiaolin He, R. Glowinski and Xiao-Ping Wang, A least square/finite element method for the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line, J. Comput. Phys., 230 (2011), 4991-5009.
doi: 10.1016/j.jcp.2011.03.022. |
[13] |
Yinnian He, Yunxian Liu and Tao Tang, On large time-stepping methods for the Cahn-Hilliard equation, Appl. Numer. Math., 57 (2007), 616-628.
doi: 10.1016/j.apnum.2006.07.026. |
[14] |
Xianliang Hu, Ruo Li and Tao Tang, A multi-mesh adaptive finite element approximation to phase field models, Commun. Comput. Phys., 5 (2009), 1012-1029. |
[15] |
J. Léopoldés, A. Dupuis, D. G. Bucknall and J. M. Yeomans, Jetting micron-scale droplets onto chemically heterogeneous surfaces, Langmuir, 19 (2003), 9818-9822.
doi: 10.1021/la0353069. |
[16] |
Xiongping Luo, Xiao-Ping Wang, Tiezheng Qian and Ping Sheng, Moving contact line over undulating surfaces, Solid. Stat. Commun., 139 (2006), 623-629.
doi: 10.1016/j.ssc.2006.04.040. |
[17] |
Nikolas Provatas, Nigel Goldenfeld and Jonathan Dantzig, Adaptive mesh refinement computation of solidification microstructures using dynamic data structures, J. Comput. Phys., 148 (1999), 265-290.
doi: 10.1006/jcph.1998.6122. |
[18] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, Molecular scale contact line hydrodynamics of immiscible flows, Phys. Rev. E, 68 (2003), 016306, 15 pp.
doi: 10.1103/PhysRevE.68.016306. |
[19] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, Molecular hydrodynamics of the moving contact line in two-phase immiscible flows, Commun. Comput. Phys., 1 (2006), 1-52. |
[20] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, A variational approach to the moving contact line hydrodynamics, J. Fluid Mech., 564 (2006), 333-360.
doi: 10.1017/S0022112006001935. |
[21] |
Jie Shen and Xiaofeng Yang, A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities, SIAM J. Sci. Comput., 32 (2010), 1159-1179.
doi: 10.1137/09075860X. |
[22] |
R. Verfurth, "A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques," Wiley-Teubner, 1996. |
[23] |
J. M. Yeomans and H.Kusumaatmaja, Modelling drop dynamics on patterned surfaces, Bull. Pol. Acad. Sci.: Tech. Sci., 55 (2007), 203-210. |
[24] |
Pengtao Yue, James J. Feng, Chun Liu and Jie Shen, A diffuse-interface method for simulating two-phase flows of complex fluids, J. Fluid Mech., 515 (2004), 293-317.
doi: 10.1017/S0022112004000370. |
[25] |
Pengtao Yue, Chunfeng Zhou, James J. Feng, Carl F. Ollivier-Gooch and Howard H. Hu, Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing, J. Comput. Phys., 219 (2006), 47-67.
doi: 10.1016/j.jcp.2006.03.016. |
[26] |
Linbo Zhang, Parallel hierarchical grid., Available from: , ().
|
[27] |
Chunfeng Zhou, Pengtao Yue and James J. Feng, 3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids, J. Comput. Phys., 229 (2010), 498-511.
doi: 10.1016/j.jcp.2009.09.039. |
[28] |
Xiao-Ping Wang, Tiezheng Qian and Ping Sheng, Moving contact line on chemically patterned surfaces, J. Fluid Mech., 605 (2008), 59-78.
doi: 10.1017/S0022112008001456. |
show all references
References:
[1] |
H. D. Ceniceros, Rudimar L. Nos and Alexandre M. Roma, Theree-dimensional, fully adaptive simulations of phase-field fluid models, J. Comput. Phys., 229 (2010), 6135-6155.
doi: 10.1016/j.jcp.2010.04.045. |
[2] |
Qingming Chang and J. I. D. Alexander, Analysis of single droplet dynamics on striped surface domains using a lattice Boltzmann method, Microfluid Nanofluid, 2 (2006), 309-326.
doi: 10.1007/s10404-005-0075-2. |
[3] |
Yana Di, Ruo Li and Tao Tang, A general moving mesh framework in 3D and its application for simulating the mixture of multi-phase flows, Commun. Comput. Phys., 3 (2008), 582-602. |
[4] |
Yana Di and Xiao-Ping Wang, Precursor simulations in spreading using a multi-mesh adaptive finite elment method, J. Comput. Phys., 228 (2009), 1380-1390.
doi: 10.1016/j.jcp.2008.10.028. |
[5] |
Q. Du and R. A. Nicolaides, Numerical analysis of a continuum model of phase transition, SIAM J. Numer. Anal., 28 (1991), 1310-1322.
doi: 10.1137/0728069. |
[6] |
Qiang Du and Jian Zhang, Adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations, SIAM J. Sci. Comput., 30 (2008), 1634-1657.
doi: 10.1137/060656449. |
[7] |
A. Dupuis and J. M. Yeomans, Droplet dynamics on patterned substrates, Pramana J. Phys., 64 (2005), 1019-1027.
doi: 10.1007/BF02704164. |
[8] |
Xiaobing Feng, Fully discrete finite element approximations of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two phase flows, SIAM J. Numer. Anal., 44 (2006), 1049-1072.
doi: 10.1137/050638333. |
[9] |
Xiaobing Feng and A. Prohl, Error analysis of a mixed finite element method for the Cahn-Hilliard equation, Numer. Math., 99 (2004), 47-84.
doi: 10.1007/s00211-004-0546-5. |
[10] |
Min Gao and Xiao-Ping Wang, A gradient stable scheme for a phase field model for the moving contact line problem, J. Comput. Phys., 231 (2012), 1372-1386.
doi: 10.1016/j.jcp.2011.10.015. |
[11] |
V. Girault and P.-A. Raviart, "Finite Element Method for Navier-Stokes Equations. Theory and Algorithms," Springer Series in Computational Mathematics, 5, Springer-Verlag, Berlin, 1986.
doi: 10.1007/978-3-642-61623-5. |
[12] |
Qiaolin He, R. Glowinski and Xiao-Ping Wang, A least square/finite element method for the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line, J. Comput. Phys., 230 (2011), 4991-5009.
doi: 10.1016/j.jcp.2011.03.022. |
[13] |
Yinnian He, Yunxian Liu and Tao Tang, On large time-stepping methods for the Cahn-Hilliard equation, Appl. Numer. Math., 57 (2007), 616-628.
doi: 10.1016/j.apnum.2006.07.026. |
[14] |
Xianliang Hu, Ruo Li and Tao Tang, A multi-mesh adaptive finite element approximation to phase field models, Commun. Comput. Phys., 5 (2009), 1012-1029. |
[15] |
J. Léopoldés, A. Dupuis, D. G. Bucknall and J. M. Yeomans, Jetting micron-scale droplets onto chemically heterogeneous surfaces, Langmuir, 19 (2003), 9818-9822.
doi: 10.1021/la0353069. |
[16] |
Xiongping Luo, Xiao-Ping Wang, Tiezheng Qian and Ping Sheng, Moving contact line over undulating surfaces, Solid. Stat. Commun., 139 (2006), 623-629.
doi: 10.1016/j.ssc.2006.04.040. |
[17] |
Nikolas Provatas, Nigel Goldenfeld and Jonathan Dantzig, Adaptive mesh refinement computation of solidification microstructures using dynamic data structures, J. Comput. Phys., 148 (1999), 265-290.
doi: 10.1006/jcph.1998.6122. |
[18] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, Molecular scale contact line hydrodynamics of immiscible flows, Phys. Rev. E, 68 (2003), 016306, 15 pp.
doi: 10.1103/PhysRevE.68.016306. |
[19] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, Molecular hydrodynamics of the moving contact line in two-phase immiscible flows, Commun. Comput. Phys., 1 (2006), 1-52. |
[20] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, A variational approach to the moving contact line hydrodynamics, J. Fluid Mech., 564 (2006), 333-360.
doi: 10.1017/S0022112006001935. |
[21] |
Jie Shen and Xiaofeng Yang, A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities, SIAM J. Sci. Comput., 32 (2010), 1159-1179.
doi: 10.1137/09075860X. |
[22] |
R. Verfurth, "A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques," Wiley-Teubner, 1996. |
[23] |
J. M. Yeomans and H.Kusumaatmaja, Modelling drop dynamics on patterned surfaces, Bull. Pol. Acad. Sci.: Tech. Sci., 55 (2007), 203-210. |
[24] |
Pengtao Yue, James J. Feng, Chun Liu and Jie Shen, A diffuse-interface method for simulating two-phase flows of complex fluids, J. Fluid Mech., 515 (2004), 293-317.
doi: 10.1017/S0022112004000370. |
[25] |
Pengtao Yue, Chunfeng Zhou, James J. Feng, Carl F. Ollivier-Gooch and Howard H. Hu, Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing, J. Comput. Phys., 219 (2006), 47-67.
doi: 10.1016/j.jcp.2006.03.016. |
[26] |
Linbo Zhang, Parallel hierarchical grid., Available from: , ().
|
[27] |
Chunfeng Zhou, Pengtao Yue and James J. Feng, 3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids, J. Comput. Phys., 229 (2010), 498-511.
doi: 10.1016/j.jcp.2009.09.039. |
[28] |
Xiao-Ping Wang, Tiezheng Qian and Ping Sheng, Moving contact line on chemically patterned surfaces, J. Fluid Mech., 605 (2008), 59-78.
doi: 10.1017/S0022112008001456. |
[1] |
Liupeng Wang, Yunqing Huang. Error estimates for second-order SAV finite element method to phase field crystal model. Electronic Research Archive, 2021, 29 (1) : 1735-1752. doi: 10.3934/era.2020089 |
[2] |
Jie Wang, Xiaoqiang Wang. New asymptotic analysis method for phase field models in moving boundary problem with surface tension. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3185-3213. doi: 10.3934/dcdsb.2015.20.3185 |
[3] |
Hao Wang, Wei Yang, Yunqing Huang. An adaptive edge finite element method for the Maxwell's equations in metamaterials. Electronic Research Archive, 2020, 28 (2) : 961-976. doi: 10.3934/era.2020051 |
[4] |
Bo You. Global attractor of the Cahn-Hilliard-Navier-Stokes system with moving contact lines. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2283-2298. doi: 10.3934/cpaa.2019103 |
[5] |
Bo You. Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021251 |
[6] |
Mei-Qin Zhan. Finite element analysis and approximations of phase-lock equations of superconductivity. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 95-108. doi: 10.3934/dcdsb.2002.2.95 |
[7] |
H. Beirão da Veiga. Vorticity and regularity for flows under the Navier boundary condition. Communications on Pure and Applied Analysis, 2006, 5 (4) : 907-918. doi: 10.3934/cpaa.2006.5.907 |
[8] |
Derrick Jones, Xu Zhang. A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces. Electronic Research Archive, 2021, 29 (5) : 3171-3191. doi: 10.3934/era.2021032 |
[9] |
Jie Liao, Xiao-Ping Wang. Stability of an efficient Navier-Stokes solver with Navier boundary condition. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 153-171. doi: 10.3934/dcdsb.2012.17.153 |
[10] |
Gang Bao, Mingming Zhang, Bin Hu, Peijun Li. An adaptive finite element DtN method for the three-dimensional acoustic scattering problem. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 61-79. doi: 10.3934/dcdsb.2020351 |
[11] |
Dongho Kim, Eun-Jae Park. Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 873-886. doi: 10.3934/dcdsb.2008.10.873 |
[12] |
Michael Hintermüller, Monserrat Rincon-Camacho. An adaptive finite element method in $L^2$-TV-based image denoising. Inverse Problems and Imaging, 2014, 8 (3) : 685-711. doi: 10.3934/ipi.2014.8.685 |
[13] |
Donatella Danielli, Marianne Korten. On the pointwise jump condition at the free boundary in the 1-phase Stefan problem. Communications on Pure and Applied Analysis, 2005, 4 (2) : 357-366. doi: 10.3934/cpaa.2005.4.357 |
[14] |
Tien-Tsan Shieh. From gradient theory of phase transition to a generalized minimal interface problem with a contact energy. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2729-2755. doi: 10.3934/dcds.2016.36.2729 |
[15] |
Abderrazak Chrifi, Mostafa Abounouh, Hassan Al Moatassime. Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 79-93. doi: 10.3934/dcdss.2021030 |
[16] |
Stefan Berres, Ricardo Ruiz-Baier, Hartmut Schwandt, Elmer M. Tory. An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks and Heterogeneous Media, 2011, 6 (3) : 401-423. doi: 10.3934/nhm.2011.6.401 |
[17] |
Wenya Qi, Padmanabhan Seshaiyer, Junping Wang. A four-field mixed finite element method for Biot's consolidation problems. Electronic Research Archive, 2021, 29 (3) : 2517-2532. doi: 10.3934/era.2020127 |
[18] |
Zhenhua Zhang. Asymptotic behavior of solutions to the phase-field equations with neumann boundary conditions. Communications on Pure and Applied Analysis, 2005, 4 (3) : 683-693. doi: 10.3934/cpaa.2005.4.683 |
[19] |
Yinnian He, Yanping Lin, Weiwei Sun. Stabilized finite element method for the non-stationary Navier-Stokes problem. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 41-68. doi: 10.3934/dcdsb.2006.6.41 |
[20] |
Yueqiang Shang, Qihui Zhang. A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3119-3142. doi: 10.3934/dcdsb.2020222 |
2020 Impact Factor: 1.639
Tools
Metrics
Other articles
by authors
[Back to Top]