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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.
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.
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.
|
[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.
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.
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.
doi: 10.1137/060656449. |
[7] |
A. Dupuis and J. M. Yeomans, Droplet dynamics on patterned substrates,, Pramana J. Phys., 64 (2005), 1019.
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.
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.
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.
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 (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.
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.
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.
|
[15] |
J. Léopoldés, A. Dupuis, D. G. Bucknall and J. M. Yeomans, Jetting micron-scale droplets onto chemically heterogeneous surfaces,, Langmuir, 19 (2003), 9818.
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.
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.
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).
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. Google Scholar |
[20] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, A variational approach to the moving contact line hydrodynamics,, J. Fluid Mech., 564 (2006), 333.
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.
doi: 10.1137/09075860X. |
[22] |
R. Verfurth, "A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques,", Wiley-Teubner, (1996). Google Scholar |
[23] |
J. M. Yeomans and H.Kusumaatmaja, Modelling drop dynamics on patterned surfaces,, Bull. Pol. Acad. Sci.: Tech. Sci., 55 (2007), 203. Google Scholar |
[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.
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.
doi: 10.1016/j.jcp.2006.03.016. |
[26] |
Linbo Zhang, Parallel hierarchical grid., Available from: , (). Google Scholar |
[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.
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.
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.
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.
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.
|
[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.
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.
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.
doi: 10.1137/060656449. |
[7] |
A. Dupuis and J. M. Yeomans, Droplet dynamics on patterned substrates,, Pramana J. Phys., 64 (2005), 1019.
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.
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.
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.
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 (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.
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.
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.
|
[15] |
J. Léopoldés, A. Dupuis, D. G. Bucknall and J. M. Yeomans, Jetting micron-scale droplets onto chemically heterogeneous surfaces,, Langmuir, 19 (2003), 9818.
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.
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.
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).
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. Google Scholar |
[20] |
Tiezheng Qian, Xiao-Ping Wang and Ping Sheng, A variational approach to the moving contact line hydrodynamics,, J. Fluid Mech., 564 (2006), 333.
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.
doi: 10.1137/09075860X. |
[22] |
R. Verfurth, "A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques,", Wiley-Teubner, (1996). Google Scholar |
[23] |
J. M. Yeomans and H.Kusumaatmaja, Modelling drop dynamics on patterned surfaces,, Bull. Pol. Acad. Sci.: Tech. Sci., 55 (2007), 203. Google Scholar |
[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.
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.
doi: 10.1016/j.jcp.2006.03.016. |
[26] |
Linbo Zhang, Parallel hierarchical grid., Available from: , (). Google Scholar |
[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.
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.
doi: 10.1017/S0022112008001456. |
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