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Volumn 229, Issue 17, 2010, Pages 6135-6155

Three-dimensional, fully adaptive simulations of phase-field fluid models

Author keywords

Adaptive mesh refinements; Bharmonic equation; Conservative phase field models; Flow induced drop coalescence; Kelvin Helmholtz instability; Model H; Multi level multigrid; Semi implicit methods

Indexed keywords

DROPS; MESH GENERATION; PHASE INTERFACES; TWO PHASE FLOW;

EID: 77953616104     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.04.045     Document Type: Article
Times cited : (66)

References (49)
  • 1
    • 0000808774 scopus 로고    scopus 로고
    • Mixing of a two-phase fluid by a cavity flow
    • Chella R., Viñals V. Mixing of a two-phase fluid by a cavity flow. Phys. Rev. E 1996, 53:3832.
    • (1996) Phys. Rev. E , vol.53 , pp. 3832
    • Chella, R.1    Viñals, V.2
  • 2
    • 0002521331 scopus 로고    scopus 로고
    • Calculation of two-phase Navier-Stokes flows using phase-field modeling
    • Jacqmin D. Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 1999, 155:96-127.
    • (1999) J. Comput. Phys. , vol.155 , pp. 96-127
    • Jacqmin, D.1
  • 3
    • 0141626836 scopus 로고    scopus 로고
    • Computation of multiphase systems with phase field models
    • Badalassi V.E., Ceniceros H.D., Banerjee S. Computation of multiphase systems with phase field models. J. Comput. Phys. 2003, 190:371-397.
    • (2003) J. Comput. Phys. , vol.190 , pp. 371-397
    • Badalassi, V.E.1    Ceniceros, H.D.2    Banerjee, S.3
  • 4
    • 10644271417 scopus 로고    scopus 로고
    • Gravitational effects on structural development in quenched complex fluids
    • Badalassi V.E., Ceniceros H.D., Banerjee S. Gravitational effects on structural development in quenched complex fluids. Ann. NY Acad. Sci. 2004, 1027:371-382.
    • (2004) Ann. NY Acad. Sci. , vol.1027 , pp. 371-382
    • Badalassi, V.E.1    Ceniceros, H.D.2    Banerjee, S.3
  • 5
    • 0346332035 scopus 로고    scopus 로고
    • Conservative multigrid methods for Cahn-Hilliard fluids
    • Kim J., Kang K., Lowengrub J. Conservative multigrid methods for Cahn-Hilliard fluids. J. Comput. Phys. 2004, 193:511-543.
    • (2004) J. Comput. Phys. , vol.193 , pp. 511-543
    • Kim, J.1    Kang, K.2    Lowengrub, J.3
  • 6
    • 85128845199 scopus 로고    scopus 로고
    • Conservative multigrid methods for ternary Cahn-Hilliard systems
    • Kim J., Kang K., Lowengrub J. Conservative multigrid methods for ternary Cahn-Hilliard systems. Commun. Math. Sci. 2004, 2:53-77.
    • (2004) Commun. Math. Sci. , vol.2 , pp. 53-77
    • Kim, J.1    Kang, K.2    Lowengrub, J.3
  • 7
    • 3142696325 scopus 로고    scopus 로고
    • Numerical study of viscoelastic mixtures through a Cahn-Hilliard flow model
    • Boyer F., Chupin L., Fabrie P. Numerical study of viscoelastic mixtures through a Cahn-Hilliard flow model. Eur. J. Mech. B/Fluids 2004, 23:759-780.
    • (2004) Eur. J. Mech. B/Fluids , vol.23 , pp. 759-780
    • Boyer, F.1    Chupin, L.2    Fabrie, P.3
  • 8
    • 5444256136 scopus 로고    scopus 로고
    • A diffuse-interface method for simulating two-phase flows of complex fluids
    • Yue P., Feng J.J., Liu C., Shen J. A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 2004, 515:293-317.
    • (2004) J. Fluid Mech. , vol.515 , pp. 293-317
    • Yue, P.1    Feng, J.J.2    Liu, C.3    Shen, J.4
  • 9
    • 26944467877 scopus 로고    scopus 로고
    • Viscoelastic effects on drop deformation in steady shear
    • Yue P., Feng J.J., Liu C., Shen J. Viscoelastic effects on drop deformation in steady shear. J. Fluid Mech. 2005, 540:427-437.
    • (2005) J. Fluid Mech. , vol.540 , pp. 427-437
    • Yue, P.1    Feng, J.J.2    Liu, C.3    Shen, J.4
  • 10
    • 26844565496 scopus 로고    scopus 로고
    • Diffuse-interface simulations of drop-coalescence and retraction in viscoelastic fluids
    • Yue P., Feng J.J., Liu C., Shen J. Diffuse-interface simulations of drop-coalescence and retraction in viscoelastic fluids. J. Non-Newtonian Fluid Dynam. 2005, 129:163-176.
    • (2005) J. Non-Newtonian Fluid Dynam. , vol.129 , pp. 163-176
    • Yue, P.1    Feng, J.J.2    Liu, C.3    Shen, J.4
  • 11
    • 33750324569 scopus 로고    scopus 로고
    • Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing
    • Yue P., Zhou C., Feng J.J., Ollivier-Gooch C.F., Hu H.H. Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing. J. Comput. Phys. 2006, 219:47-67.
    • (2006) J. Comput. Phys. , vol.219 , pp. 47-67
    • Yue, P.1    Zhou, C.2    Feng, J.J.3    Ollivier-Gooch, C.F.4    Hu, H.H.5
  • 14
    • 85190572566 scopus 로고
    • Capillary action, in: Encyclopaedia Britannica, 9th ed., 1876, reprinted in The Scientific Papers of James Clerk Maxwell, Dover, New York
    • J.C. Maxwell, Capillary action, in: Encyclopaedia Britannica, 9th ed., 1876, reprinted in The Scientific Papers of James Clerk Maxwell, Dover, New York, 1951.
    • (1951)
    • Maxwell, J.C.1
  • 15
    • 0000063775 scopus 로고
    • On the equilibrium of heterogeneous substances, Trans. Conn. Acad. reprinted in The Scientific Papers of
    • J.W. Gibbs, On the equilibrium of heterogeneous substances, Trans. Conn. Acad. 3 (1876) 108-248 (reprinted in The Scientific Papers of J. Willard Gibbs, Longman, Green, London, 1906).
    • (1876) J. Willard Gibbs, Longman, Green, London , vol.3 , pp. 108-248
    • Gibbs, J.W.1
  • 16
    • 0001407145 scopus 로고
    • On the theory of surface forces-II. Compressible fluids
    • Rayleigh Lord On the theory of surface forces-II. Compressible fluids. Philos. Mag. 1892, 33:209.
    • (1892) Philos. Mag. , vol.33 , pp. 209
    • Rayleigh, L.1
  • 17
    • 33745562760 scopus 로고
    • The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, Verhandel. Konink. Akad. Weten. (Amsterdam) 1 (1893) 8 (originally published in Dutch. Translation published by J.S. Rowlinson
    • J.D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, Verhandel. Konink. Akad. Weten. (Amsterdam) 1 (1893) 8 (originally published in Dutch. Translation published by J.S. Rowlinson, J. Stat. Phys. 20 (1979) 200-244).
    • (1979) J. Stat. Phys , vol.20 , pp. 200-244
    • van der Waals, J.D.1
  • 18
    • 0000707473 scopus 로고    scopus 로고
    • Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: application of a semi-implicit Fourier spectral method
    • Zhu J., Chen L.Q., Shen J., Tikare V. Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: application of a semi-implicit Fourier spectral method. Phys. Rev. E 1999, 60(4):3564-3572.
    • (1999) Phys. Rev. E , vol.60 , Issue.4 , pp. 3564-3572
    • Zhu, J.1    Chen, L.Q.2    Shen, J.3    Tikare, V.4
  • 19
    • 0003081461 scopus 로고    scopus 로고
    • The Cahn-Hilliard equation with elasticity: finite element approximation and qualitative studies
    • Garcke H., Rumpf M., Weikard U. The Cahn-Hilliard equation with elasticity: finite element approximation and qualitative studies. Interfaces Free Bound. 2001, 3:101-118.
    • (2001) Interfaces Free Bound. , vol.3 , pp. 101-118
    • Garcke, H.1    Rumpf, M.2    Weikard, U.3
  • 20
    • 33747854490 scopus 로고    scopus 로고
    • Application of mortar elements to diffuse-interface methods
    • Barosan I., Anderson P.D., Meijer H.E.H. Application of mortar elements to diffuse-interface methods. Comput. Fluids 2006, 35:1384-1399.
    • (2006) Comput. Fluids , vol.35 , pp. 1384-1399
    • Barosan, I.1    Anderson, P.D.2    Meijer, H.E.H.3
  • 21
    • 34547518008 scopus 로고    scopus 로고
    • A nonstiff, adaptive mesh refinement-based method for the Cahn-Hilliard equation
    • Ceniceros H.D., Roma A.M. A nonstiff, adaptive mesh refinement-based method for the Cahn-Hilliard equation. J. Comput. Phys. 2007, 225(2):1849-1862.
    • (2007) J. Comput. Phys. , vol.225 , Issue.2 , pp. 1849-1862
    • Ceniceros, H.D.1    Roma, A.M.2
  • 22
  • 23
    • 0038934567 scopus 로고    scopus 로고
    • Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de NavierStokes par une technique de projection incrémentale
    • Guermond J.L. Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de NavierStokes par une technique de projection incrémentale. M2AN Math. Model. Numer. Anal. 1999, 33(1):169189.
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , Issue.1 , pp. 169189
    • Guermond, J.L.1
  • 24
    • 0001875899 scopus 로고    scopus 로고
    • The accuracy of the fractional step method
    • Strikwerda J.C., Lee Y.S. The accuracy of the fractional step method. SIAM J. Numer. Anal. 1999, 37(1):3747.
    • (1999) SIAM J. Numer. Anal. , vol.37 , Issue.1 , pp. 3747
    • Strikwerda, J.C.1    Lee, Y.S.2
  • 25
    • 77950177924 scopus 로고    scopus 로고
    • A robust, fully adaptive hybrid level-set/front-tracking method for two-phase flows with an accurate surface tension computation
    • Ceniceros H.D., Roma A.M., Silveira-Neto A., Villar M.M. A robust, fully adaptive hybrid level-set/front-tracking method for two-phase flows with an accurate surface tension computation. Commun. Comput. Phys. 2010, 8:51-94.
    • (2010) Commun. Comput. Phys. , vol.8 , pp. 51-94
    • Ceniceros, H.D.1    Roma, A.M.2    Silveira-Neto, A.3    Villar, M.M.4
  • 26
    • 56449118512 scopus 로고    scopus 로고
    • Adaptive pseudospectral solution of a diffuse interface model
    • Tapia J.J., Gilberto López P. Adaptive pseudospectral solution of a diffuse interface model. J. Comput. Phys. 2009, 224:101-117.
    • (2009) J. Comput. Phys. , vol.224 , pp. 101-117
    • Tapia, J.J.1    Gilberto López, P.2
  • 27
    • 35949034972 scopus 로고
    • Theory of dynamic critical phenomena
    • Hohenberg P.C., Halperin B.I. Theory of dynamic critical phenomena. Rev. Mod. Phys. 1977, 49(3):435.
    • (1977) Rev. Mod. Phys. , vol.49 , Issue.3 , pp. 435
    • Hohenberg, P.C.1    Halperin, B.I.2
  • 28
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system I
    • Cahn J.W., Hilliard J.E. Free energy of a nonuniform system I. J. Chem. Phys. 1958, 28:258.
    • (1958) J. Chem. Phys. , vol.28 , pp. 258
    • Cahn, J.W.1    Hilliard, J.E.2
  • 29
    • 0013356201 scopus 로고
    • Free energy of a nonuniform system III
    • Cahn J.W., Hilliard J.E. Free energy of a nonuniform system III. J. Chem. Phys. 1959, 31:688.
    • (1959) J. Chem. Phys. , vol.31 , pp. 688
    • Cahn, J.W.1    Hilliard, J.E.2
  • 30
    • 77951945499 scopus 로고    scopus 로고
    • 3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids
    • Zhou C., Yue P., Feng J.J., Ollivier-Gooch C.F., Hu H.H. 3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids. J. Comput. Phys. 2010, 229:498-511.
    • (2010) J. Comput. Phys. , vol.229 , pp. 498-511
    • Zhou, C.1    Yue, P.2    Feng, J.J.3    Ollivier-Gooch, C.F.4    Hu, H.H.5
  • 31
    • 0036469249 scopus 로고    scopus 로고
    • Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration
    • Lee H., Lowengrub J.S., Goodman J. Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration. Phys. Fluids 2002, 14(2):492.
    • (2002) Phys. Fluids , vol.14 , Issue.2 , pp. 492
    • Lee, H.1    Lowengrub, J.S.2    Goodman, J.3
  • 33
    • 0346505865 scopus 로고
    • Theory of phase-ordering kinetics
    • Bray A.J. Theory of phase-ordering kinetics. Adv. Phys. 1994, 43(3):357-459.
    • (1994) Adv. Phys. , vol.43 , Issue.3 , pp. 357-459
    • Bray, A.J.1
  • 34
    • 0001575645 scopus 로고    scopus 로고
    • Two-phase binary fluids and immiscible fluids described by an order parameter
    • Gurtin M.E., Polignone D., Viñals J. Two-phase binary fluids and immiscible fluids described by an order parameter. Math. Models Methods Appl. Sci. 1996, 6(6):815.
    • (1996) Math. Models Methods Appl. Sci. , vol.6 , Issue.6 , pp. 815
    • Gurtin, M.E.1    Polignone, D.2    Viñals, J.3
  • 35
    • 0041152882 scopus 로고    scopus 로고
    • Quasi-incompressible Cahn-Hilliard fluids and topological transitions
    • Lowengrub J., Truskinovsky L. Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Proc. R. Soc. London A 1998, 454:2617.
    • (1998) Proc. R. Soc. London A , vol.454 , pp. 2617
    • Lowengrub, J.1    Truskinovsky, L.2
  • 36
    • 0036028061 scopus 로고    scopus 로고
    • A theoretical and numerical model for the study of incompressible mixture flows
    • Boyer F. A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 2002, 31(1):41.
    • (2002) Comput. Fluids , vol.31 , Issue.1 , pp. 41
    • Boyer, F.1
  • 37
    • 34547512592 scopus 로고    scopus 로고
    • Stability analysis of large time-stepping methods for epitaxial growth models
    • Xu C., Tang T. Stability analysis of large time-stepping methods for epitaxial growth models. SIAM J. Numer. Anal. 2006, 44(4):1759-1779.
    • (2006) SIAM J. Numer. Anal. , vol.44 , Issue.4 , pp. 1759-1779
    • Xu, C.1    Tang, T.2
  • 38
    • 11744289966 scopus 로고
    • Local adaptive mesh refinement for shock hydrodynamics
    • Berger M.J., Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 1989, 82:64-84.
    • (1989) J. Comput. Phys. , vol.82 , pp. 64-84
    • Berger, M.J.1    Colella, P.2
  • 39
    • 0026226856 scopus 로고
    • An algorithm for point clustering and grid generation
    • Berger M.J., Rigoutsos I. An algorithm for point clustering and grid generation. IEEE Trans. Syst. Man Cybernet. 1991, 21(5):1278-1286.
    • (1991) IEEE Trans. Syst. Man Cybernet. , vol.21 , Issue.5 , pp. 1278-1286
    • Berger, M.J.1    Rigoutsos, I.2
  • 40
    • 85190568487 scopus 로고    scopus 로고
    • Solução de equações diferenciais parciais elípticas por técnicas multinível-multigrid em malhas tridimensionais bloco-estruturadas com refinamento localizado, in: Anais do XXVIII Congresso Nacional de Ma
    • R.L. Nós, A.M. Roma, H.D. Ceniceros, Solução de equações diferenciais parciais elípticas por técnicas multinível-multigrid em malhas tridimensionais bloco-estruturadas com refinamento localizado, in: Anais do XXVIII Congresso Nacional de Matemática Aplicada e Computacional, São Paulo, 2005.
    • Nós, R.L.1    Roma, A.M.2    Ceniceros, H.D.3
  • 41
    • 17144401291 scopus 로고    scopus 로고
    • Study of the long-time dynamics of a viscous vortex sheet with a fully adaptive non-stiff numerical method
    • Ceniceros H.D., Roma A.M. Study of the long-time dynamics of a viscous vortex sheet with a fully adaptive non-stiff numerical method. Phys. Fluids 2004, 16(12):4285-4318.
    • (2004) Phys. Fluids , vol.16 , Issue.12 , pp. 4285-4318
    • Ceniceros, H.D.1    Roma, A.M.2
  • 42
    • 85190568716 scopus 로고    scopus 로고
    • Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo de fase, Ph.D. Thesis, Universidade de São Paulo, Brasil
    • R.L. Nós, Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo de fase, Ph.D. Thesis, Universidade de São Paulo, Brasil, 2007.
    • (2007)
    • Nós, R.L.1
  • 43
    • 0021122168 scopus 로고
    • The deformation of small viscous drops and bubbles in shear flows
    • Rallison J.M. The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 1984, 16:45-66.
    • (1984) Annu. Rev. Fluid Mech. , vol.16 , pp. 45-66
    • Rallison, J.M.1
  • 44
    • 0002532545 scopus 로고
    • Dynamics of drop deformation and breakup in viscous fluids
    • Stone H.A. Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 1994, 26:65-102.
    • (1994) Annu. Rev. Fluid Mech. , vol.26 , pp. 65-102
    • Stone, H.A.1
  • 45
    • 0002994075 scopus 로고
    • The viscosity of a fluid containing small drops of another fluid
    • Taylor G.I. The viscosity of a fluid containing small drops of another fluid. R. Soc. London Proc. Ser. A 1932, 138:41-48.
    • (1932) R. Soc. London Proc. Ser. A , vol.138 , pp. 41-48
    • Taylor, G.I.1
  • 46
    • 0031177712 scopus 로고    scopus 로고
    • Structures in stratified plane mixing layers and the effects of cross-shear
    • Atsavapranee P., Gharib M. Structures in stratified plane mixing layers and the effects of cross-shear. J. Fluid Mech. 1997, 342:53-86.
    • (1997) J. Fluid Mech. , vol.342 , pp. 53-86
    • Atsavapranee, P.1    Gharib, M.2
  • 47
    • 50249101609 scopus 로고    scopus 로고
    • An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
    • Hou T.Y., Shi Z. An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. J. Comput. Phys. 2008, 227:8968-8991.
    • (2008) J. Comput. Phys. , vol.227 , pp. 8968-8991
    • Hou, T.Y.1    Shi, Z.2
  • 49
    • 0034260316 scopus 로고    scopus 로고
    • A boundary condition capturing method for multiphase incompressible flow
    • Kang M., Fedkiw R.P., Liu X. A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 2000, 15:323-360.
    • (2000) J. Sci. Comput. , vol.15 , pp. 323-360
    • Kang, M.1    Fedkiw, R.P.2    Liu, X.3


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