Efficient and structure-preserving time-dependent auxiliary variable method for a conservative Allen–Cahn type surfactant system (original) (raw)

• James AJ, Lowengrub J (2014) A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. J Comput Phys 201(2):685–772
  Article MathSciNet MATH Google Scholar
• Cleret de Langavant C, Guittet A, Theillard M, Temprano-Coleto F, Gibou F (2017) Level-set simulations of soluble surfactant deriven flows. J Comput Phys 348:271–297
  Article MathSciNet MATH Google Scholar
• Xu JJ, Shi W, Lai MC (2018) A level-set method for two-phase flows with soluble surfactant. J Comput Phys 353:336–355
  Article MathSciNet MATH Google Scholar
• Hu WF, Lai MC, Misbah C (2018) A coupled immersed boundary and immersed interface method for interfacial flows with soluble surfactant. Comput Fluids 168:201–215
  Article MathSciNet MATH Google Scholar
• Seol Y, Hsu SH, Lai MC (2018) An immersed boundary method for simulating interfacial flows with insoluble surfactant in three dimensions. Commun Comput Phys 23:640–664
  Article MathSciNet MATH Google Scholar
• Laradji M, Guo H, Grant M, Zuckermann MJ (1992) The effect of surfactants on the dynamics of phase separation. J Phys Condens Matter 32(4):6715
  Article Google Scholar
• Guo Z, Yu F, Lin P, Wise S, Lowengrub J (2021) A diffuse domain method for two-phase flows with large density ratio in complex geometries. J Fluid Mech 907:A38
  Article MathSciNet MATH Google Scholar
• Rebholz L, Wise SM, Xiao M (2018) Penalty-projection schemes for the Cahn-Hilliard-Navier-Stokes diffuse interface model of two phase flow and their connection to divergence-free schemes. Int J Numer Anal Model 15:649–676
  MathSciNet MATH Google Scholar
• Yang J, Kim J (2020) An unconditionally stable second-order accurate method for systems of Cahn-Hilliard equations. Commun Nonlinear Sci Numer Simulat 87:105276
  Article MathSciNet MATH Google Scholar
• Liang H, Shi BC, Chai ZH (2016) Lattice Boltzmann modeling of three-phase incompressible flows. Phys Rev E 93:013308
  Article MathSciNet Google Scholar
• Liang H, Xu J, Chen J, Chai Z, Shi B (2019) Lattice Boltzmann modeling of wall-bounded ternary fluid flows. Appl Math Model 73:487–513
  Article MathSciNet MATH Google Scholar
• Kim J (2006) Numerical simulations of phase separation dynamics in a water-oil-surfactant system. J Colloid Interf Sci 303:272–279
  Article Google Scholar
• Gu S, Zhang H, Zhang Z (2014) An energy-stable finite-difference scheme for the binary fluid-surfactant system. J Comput Phys 270:416–431
  Article MathSciNet MATH Google Scholar
• Chen W, Wang C, Wang S, Wang X, Wise SM (2020) Energy stable numerical schemes for ternary Cahn-Hilliard system. J Sci Comput 84:27
  Article MathSciNet MATH Google Scholar
• Cheng K, Wang C, Wise SM (2020) A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis. J Comput Phys 405:109109
  Article MathSciNet MATH Google Scholar
• Shin J, Lee HG (2021) A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection. Appl Numer Math 163:30–42
  Article MathSciNet MATH Google Scholar
• Liu Z, Li X (2020) Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation. Numer Algor 85:107–132
  Article MathSciNet MATH Google Scholar
• Liu Z, Li X (2019) Efficient modified techniques of invariant energy quadratization approach for gradient flows. Appl Math Lett 98:206–214
  Article MathSciNet MATH Google Scholar
• Liu Z, Li X (2020) The exonential scalr auxiliary variable (E-SAV) approach for phase field models and its explicit computing. SIAM J Sci Comput 42(3):B630–B655
  Article MATH Google Scholar
• Zhang C, Ouyang J, Wang C, Wise SM (2020) Numerical comparison of modified-energy stable SAV-type schemes and classical BDF methods on benchmark problems for the functionalized Cahn-Hilliard equation. J Comput Phys 423:109772
  Article MathSciNet MATH Google Scholar
• Li Q, Mei L (2021) Efficient, decoupled, and second-order unconditionally energy stable numerical schemes for the coupled Cahn-Hilliard system in copolymer/homopolymer mixtures. Comput Phys Commun 260:107290
  Article MathSciNet Google Scholar
• Yang J, Kim J (2021) An improved scalar auxiliary variable (SAV) approach for the phase-field surfactant model. Appl Math Model 90:11–29
  Article MathSciNet MATH Google Scholar
• Qin Y, Xu Z, Zhang H, Zhang Z (2020) Fully decoupled, linear and unconditionally energy stable schemes for the binary fluid-surfactant model. Commun Comput Phys 28:1389–1414
  Article MathSciNet MATH Google Scholar
• Zhu G, Kou J, Yao J, Li A, Sun S (2020) A phase-field moving contact line model with soluble surfactants. J Comput Phys 405:109170
  Article MathSciNet MATH Google Scholar
• Aihara B, Takaki T, Takada D (2019) Multi-phase-field modeling using a conservative Allen-Cahn equation for multiphase flow. Comput Fluid 178:141–151
  Article MathSciNet MATH Google Scholar
• Begmohammadi A, Haghani-Hassan-Abadi R, Fakhari A, Bolster D (2020) Study of phase-field lattice Boltzmann models based on the conservative Allen-Cahn equation. Phys Rev E 102:023305
  Article MathSciNet Google Scholar
• Weng Z, Zhuang Q (2017) Numerical approximation of the conservative Allen-Cahn equation by operator splitting method. Math Methods Appl Sci 40(12):4462–4480
  Article MathSciNet MATH Google Scholar
• Huang Z, Lin G, Ardekani AM (2020) Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model. J Comput Phys 420:109718
  Article MathSciNet MATH Google Scholar
• Yang J, Jeong D, Kim J (2021) A fast and practical adaptive finite difference method for the conservative Allen-Cahn model in two-phase flow system. Int J Multiphase Flow 137:103561
  Article MathSciNet Google Scholar
• Zheng L, Zheng S, Zhai Q (2020) Multiphase flows of \(N\) immiscible incompressible fluids: conservative Allen-Cahn equation and lattice Boltzmann equation method. Phys Rev E 101:013305
  Article Google Scholar
• Yang J, Kim J (2021) A variant of stabilized-scalar auxiliary variable (S-SAV) approach for a modified phase-field surfactant model. Comput Phys Commun 261:107825
  Article MathSciNet Google Scholar
• Liao HL, Tang T, Zhou T (2020) On energy stable, miximum-pribciple preserving, second-order BDF scheme with variable steps for the Allen-Cahn equation. SIAM J Numer Anal 58(4):2294–2314
  Article MathSciNet MATH Google Scholar
• Shen J, Xu J, Yang J (2018) The scalar auxiliary variable (SAV) approach for gradient flows. J Comput Phys 353:407–416
  Article MathSciNet MATH Google Scholar
• Cheng Q, Liu C, Shen J (2020) A new Lagrange multiplier approach for gradient flows. Comput Methods Appl Mech Eng 367:113070
  Article MathSciNet MATH Google Scholar
• Han S, Ye Q, Yang X (2021) Highly efficient and stable numerical algorithms for a two-component phase-field crystal model for binary alloys. J Comput Appl Math 390:113371
  Article MathSciNet MATH Google Scholar
• Yang X (2021) 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 432:110015
  Article MathSciNet MATH Google Scholar
• Yang X (2021) On a novel fully-decoupled, linear and second-order accurate numerical scheme for the Cahn-Hilliard-Darcy system of two-phase Hele-Shaw flow. Comput Phys Commun 263:107868
  Article MathSciNet Google Scholar
• Shin J, Kim S, Lee D, Kim J (2013) A parallel multigrid method of the Cahn-Hilliard equation. Comput Mater Sci 71:89–96
  Article Google Scholar
• Sun M, Feng X, Wang K (2020) Numerical simulation of binary fluid-surfactant phase field model coupled with geometric curvature on the curved surface. Comput Methods Appl Mech Eng 367:113123
  Article MathSciNet MATH Google Scholar
• Zhang M, Xiao X, Feng X (2020) Numerical simulations for the predator-prey model on surfaces with lumped mass method. Eng Comput. https://doi.org/10.1007/s00366-019-00929-4
• Qiao Y, Qian L, Feng X (2021) Fast numerical approximation for the space-fractional semilinear parabolic equations on surfaces. Eng Comput. https://doi.org/10.1007/s00366-021-01357-z