EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 5 (September-October 2021) ESAIM: M2AN, 55 5 (2021) 2323-2347 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 2323 - 2347
DOI https://doi.org/10.1051/m2an/2021056
Published online 21 October 2021
  1. H. Abels, H. Garcke and G. Grün, Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Math. Models Methods Appl. Sci. 22 (2012) 1150013, 40. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Alizadeh, S.M. Seyyedi, M. Taeibi Rahni and D.D. Ganji, Three-dimensional numerical simulation of rising bubbles in the presence of cylindrical obstacles, using lattice boltzmann method. J. Mol. Liq. 236 (2017) 151–161. [CrossRef] [Google Scholar]
  3. D. Bhaga and M.E. Weber, Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech. 105 (1981) 61–85. [CrossRef] [Google Scholar]
  4. F. Boyer and S. Minjeaud, Numerical schemes for a three component Cahn-Hilliard model. ESAIM: M2AN 45 (2011) 697–738. [CrossRef] [EDP Sciences] [Google Scholar]
  5. G. Brereton and D. Korotney, Coaxial and oblique coalescence of two rising bubbles, edited by I. Sahin and G. Tryggvason. In: Dynamics of Bubbles and Vortices Near a Free Surface, AMD-Vol. ASME, New York (1991). [Google Scholar]
  6. Y. Cai and J. Shen, Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. Math. Comput. 87 (2018) 2057–2090. [Google Scholar]
  7. C. Chen and X. Yang, Efficient numerical scheme for a dendritic solidification phase field model with melt convection. J. Comput. Phys. 388 (2019) 41–62. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Chen and X. Yang, Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard Model. Comput. Meth. Appl. Mech. Eng. 351 (2019) 35–59. [Google Scholar]
  9. W. Chen, Y. Liu, C. Wang and S. Wise, Convergence analysis of a fully discrete finite difference scheme for cahn-hilliard-hele-shaw equation. Math. Comput. 85 (2016) 2231–2257. [Google Scholar]
  10. A. Diegel, C. Wang, X. Wang and S. Wise, Convergence analysis and error estimates for a second order accurate finite element method for the Cahn–Hilliard–Navier–Stokes system. Numer. Math. 137 (2017) 495–534. [CrossRef] [MathSciNet] [Google Scholar]
  11. H. Ding, P.D.M. Spelt and C. Shu, Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comput. Phys. 226 (2007) 2078–2095. [CrossRef] [Google Scholar]
  12. Q. Du and R.A. Nicolaides, Numerical analysis of a continuum model of phase transition. SIAM J. Numer. Anal. 28 (1991) 1310–1322. [Google Scholar]
  13. M. Gao and X.-P. Wang, An efficient scheme for a phase field model for the moving contact line problem with variable density and viscosity. J. Comput. Phys. 272 (2014) 704–718. [CrossRef] [MathSciNet] [Google Scholar]
  14. V. Girault and P.A. Raviart, Finite Element Method for Navier–Stokes Equations: Theory and Algorithms. Springer-Verlag, Berlin, Heidelberg (1987) 395–414. [Google Scholar]
  15. H. Gomez, D.Z. Van and G. Kristoffer, Computational phase-field modeling, 2nd edition. In: Encyclopedia of Computational Mechanics. John Wiley & Sons, Ltd. (2017). [Google Scholar]
  16. G. Grün and F. Klingbeil, Two-phase flow with mass density contrast: stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface model. J. Comput. Phys. 257 (2014) 708–725. [Google Scholar]
  17. J.L. Guermond and P. Minev, Higher-order time stepping for the incompressible Naveri-Stokes equations. SIAM. J. Sci. Comput. 37 (2015) A2656–A2681. [CrossRef] [Google Scholar]
  18. J.L. Guermond and L. Quartapelle, A projection fem for variable density incompressible flows. J. Comput. Phys. 165 (2000) 167–188. [CrossRef] [MathSciNet] [Google Scholar]
  19. J.L. Guermond and A. Salgado, A splitting method for incompressible flows with variable density based on a pressure Poisson equation. J. Comput. Phys. 228 (2009) 2834–2846. [Google Scholar]
  20. J.L. Guermond and A.J. Salgado, Error analysis of a fractional time-stepping technique for incompressible flows with variable density. SIAM J. Numer. Anal. 49 (2011) 917–944. [CrossRef] [MathSciNet] [Google Scholar]
  21. D. Han and X. Wang, A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn–Hilliard–Navier–Stokes equation. J. Comput. Phys. 290 (2015) 139–156. [CrossRef] [MathSciNet] [Google Scholar]
  22. D. Jacqmin, Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comput. Phys. 155 (2007) 96–127. [Google Scholar]
  23. D. Li, Z. Qiao and T. Tang, Characterizing the stabilization size for semi-implicit fourier-spectral method to phase field equations. SIAM J. Numer. Anal. 54 (2016) 1653–1681. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Li, Y. Cheng, J. Shen and X. Zhang, A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations. J. Comput. Phys. 425 (2021) 109906. [CrossRef] [Google Scholar]
  25. C. Liu, J. Shen and X. Yang, Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. J. Sci. Comput. 62 (2015) 601–622. [CrossRef] [MathSciNet] [Google Scholar]
  26. Y. Liu, W. Chen, C. Wang and S. Wise, Error analysis of a mixed finite element method for a Cahn–Hilliard–Hele–Shaw system. Numer. Math. 135 (2017) 679–709. [CrossRef] [MathSciNet] [Google Scholar]
  27. S. Minjeaud, An unconditionally stable uncoupled scheme for a triphasic Cahn–Hilliard/Navier–Stokes model. Numer. Methods Part. Differ. Equ. 29 (2013) 584–618. [CrossRef] [Google Scholar]
  28. R. Nochetto and J.-H. Pyo, The Gauge-Uzawa finite element method part I: the Navier-Stokes equations. SIAM J. Numer. Anal. 43 (2005) 1043–1068. [CrossRef] [MathSciNet] [Google Scholar]
  29. J. Pyo and J. Shen, Gauge-Uzawa methods for incompressible flows with variable density. J. Comput. Phys. 221 (2007) 181–197. [CrossRef] [MathSciNet] [Google Scholar]
  30. I. Romero, Thermodynamically consistent time stepping algorithms for nonlinear thermomechanical systems. Int. J. Numer. Meth. Eng. 79 (2009) 706–732. [CrossRef] [Google Scholar]
  31. J. Shen and X. Yang, Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Disc. Cont. Dyn. Sys. A 28 (2010) 1669–1691. [CrossRef] [Google Scholar]
  32. J. Shen and X. Yang, A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscositites. SIAM J. Sci. Comput. 32 (2010) 1159–1179. [CrossRef] [MathSciNet] [Google Scholar]
  33. J. Shen and X. Yang, Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. SIAM J. Num. Anal. 53 (2015) 279–296. [CrossRef] [Google Scholar]
  34. G. Tryggvason, Numerical simulations of the Rayleigh-Taylor instability. J. Comput. Phys. 75 (1988) 253–282. [CrossRef] [Google Scholar]
  35. X. Yang, Linear, first and second order and unconditionally energy stable numerical schemes for the phase field model of homopolymer blends. J. Comput. Phys. 327 (2016) 294–316. [CrossRef] [MathSciNet] [Google Scholar]
  36. X. Yang, A new efficient fully-decoupled and second-order time-accurate scheme for Cahn-Hilliard phase-field model of three-phase incompressible flow. Comput. Methods Appl. Mech. Eng. 376 (2021) 13589. [Google Scholar]
  37. X. Yang, A novel fully-decoupled, second-order and energy stable numerical scheme of the conserved Allen-Cahn type flow-coupled binary surfactant model. Comput. Methods Appl. Mech. Eng. 373 (2021) 113502. [CrossRef] [Google Scholar]
  38. X. Yang, A novel fully-decoupled, second-order time-accurate, unconditionally energy stable scheme for a flow-coupled volume-conserved phase-field elastic bending energy model. J. Comput. Phys. 432 (2021) 110015. [CrossRef] [Google Scholar]
  39. X. Yang, Fully-discrete spectral-Galerkin scheme with decoupled structure and second-order time accuracy for the anisotropic phase-field dendritic crystal growth model. Int. J. Heat Mass Transfer 180 (2021) 121750. [CrossRef] [Google Scholar]
  40. X. Yang, 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. Comput. Methods Appl. Mech. Eng. 375 (2021) 113600. [CrossRef] [Google Scholar]
  41. X. Yang, On a novel full decoupling, linear, second-order accurate, and unconditionally energy stable numerical scheme for the anisotropic phase-field dendritic crystal growth model. Int. J. Numer. Methods Eng. 122 (2021) 4129–4153. [CrossRef] [Google Scholar]
  42. X. Yang and H. Yu, Efficient second order unconditionally stable schemes for a phase field moving contact line model using an invariant energy quadratization approach. SIAM J. Sci. Comput. 40 (2018) B889–B914. [CrossRef] [Google Scholar]
  43. X. Yang and G.-D. Zhang, Convergence analysis for the invariant energy quadratization (IEQ) schemes for solving the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential. J. Sci. Comput. 82 (2020) 55. [CrossRef] [Google Scholar]
  44. H. Yu and X. Yang, Decoupled energy stable schemes for phase field model with contact lines and variable densities. J. Comput. Phys. 334 (2017) 665–686. [CrossRef] [MathSciNet] [Google Scholar]
  45. P. Yue, J. Feng, C. Liu and J. Shen, A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515 (2005) 293–317. [Google Scholar]
  46. G.-D. Zhang, X. He and X. Yang, Decoupled, linear, and unconditionally energy stable fully-discrete finite element numerical scheme for a two-phase ferrohydrodynamics model. SIAM J. Sci. Comput. 43 (2021) B167–B193. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you