Highly efficient variant of SAV approach for two-phase incompressible conservative Allen–Cahn fluids (original) (raw)
Ren H, Zhuang X, Oterkus E, Zhu H, Rabczuk T (2021) Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method. Eng Comput. https://doi.org/10.1007/s00366-021-01502-8
Abbaszadeh M, Dehghan M (2021) The fourth-order time-discrete scheme and split-step direct meshless finite volume method for solving cubic-quintic complex Ginzburg-Landau equations on complicated geometries. Eng Comput. https://doi.org/10.1007/s00366-020-01089-6
Zong Y, Zhang C, Liang H, Wang L, Xu J (2020) Modeling surfactant-laden droplet dynamics by lattice Boltzmann method. Phys Fluids 32:122105 Google Scholar
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
Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys 28(2):258–267 MATH Google Scholar
Xia Q, Yu Q, Li Y (2021) A second-order accurate, unconditionally energy stable numerical scheme for binary fluid flows on arbitrarily curved surfaces. Comput Methods Appl Mech Eng 384:113987 MathSciNetMATH Google Scholar
Gong Y, Zhao J, Wang Q (2017) An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities. Commun Comput Phys 219:20–34 MathSciNetMATH 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 MathSciNetMATH Google Scholar
Chiu P-H (2019) A coupled phase field framework for solving incompressible two-phase flows. J Comput Phys 392:115–140 MathSciNetMATH Google Scholar
Han D, Brylev A, Yang X, Tan Z (2017) Numerical analysis of second-order, fully discrete energy stable schemes for phase field models of two-phase incompressible flows. J Sci Comput 70:965–989 MathSciNetMATH Google Scholar
Li H-L, Liu H-R, Ding H (2020) A fully 3D simulation of fluid-structure interaction with dynamic wetting and contact angle hysteresis. J Comput Phys 420:109709 MathSciNetMATH Google Scholar
Bai F, Han D, He X, Yang X (2020) Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields. Commun Nonlinear Sci Numer Simul 85:105213 MathSciNetMATH Google Scholar
Yan Y, Chen W, Wang C, Wise SM (2018) A second-order energy stable BDF numerical scheme for the Cahn–Hilliard equation. Commun Comput Phys 23(2):572–602 MathSciNetMATH Google Scholar
Cheng K, Feng W, Wang C, Wise SM (2019) An energy stable fourth order finite difference scheme for the Cahn–Hilliard equation. J Comput Appl Math 362:574–595 MathSciNetMATH Google Scholar
Chen W, Feng W, Liu Y, Wang C, Wise SM (2019) A second order energy stable scheme for the Cahn–Hilliard–Hele–Shaw equations. Discrete Contin Dyn Syst Ser B 24(1):149–182 MathSciNetMATH 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 MathSciNetMATH Google Scholar
Guo J, Wang C, Wise SM, Yue X (2016) An \(H^2\) convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn–Hilliard equation. Commun Math Sci 14(2):489–515 MathSciNetMATH Google Scholar
Diegel AE, Wang C, Wise SM (2016) Stability and convergence of a second-order mixed finite element method for the Cahn–Hilliard equation. IMA J Numer Anal 36(4):1867–1897 MathSciNetMATH Google Scholar
Cheng K, Wang C, Wise SM, Yue X (2016) A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn–Hilliard equation and its solution by the homogeneous linear iteration method. J Sci Comput 69:1083–1114 MathSciNetMATH Google Scholar
Guo J, Wang C, Wise SM, Yue X (2021) An improved error analysis for a second-order numerical scheme for the Cahn–Hilliard equation. J Comput Appl Math 388:113300 MathSciNetMATH Google Scholar
Zhao S, Xiao X, Feng X (2020) A efficient time adaptivity based on chemical potential for surface Cahn–Hilliard equation using finite element approximation. Appl Math Comput 369:124901 MathSciNetMATH 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 MathSciNetMATH Google Scholar
Li X, Ju L, Meng X (2019) Convergence analysis of exponential time differencing schemes for the Cahn–Hilliard equation. Commun Comput Phys 26(5):1510–1529 MathSciNetMATH Google Scholar
Gong Y, Zhao J, Wang Q (2020) Arbitrarily high-order linear energy stable schemes for gradient flow models. J Comput Phys 419:109610 MathSciNetMATH Google Scholar
Liu Z, Li X (2019) Efficient modified techniques of invariant energy quadratization approach for gradient flows. Appl Math Lett 98:206–214 MathSciNetMATH Google Scholar
Zhu G, Chen H, Yao J, Sun S (2019) Efficient energy-stable schemes for the hydrodynamics coupled phase-field model. Appl Math Model 70:82–108 MathSciNetMATH Google Scholar
Liu Z, Li X (2020) The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation. Methods Partial Differ Equ Numer. https://doi.org/10.1002/num.22527
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 MathSciNetMATH 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 MathSciNetMATH Google Scholar
Han D, Jiang N (2020) A second order, linear, unconditionally stable, Crank–Nicolson–Leapfrog scheme for phase field models of two-phase incompressible flows. Appl Math Lett 108:106521 MathSciNetMATH Google Scholar
Chen L, Zhao J (2020) A novel second-order linear scheme for the Cahn–Hilliard–Navier–Stokes equations. J Comput Phys 423:109782 MathSciNetMATH Google Scholar
Wang X, Kou J, Gao H (2021) Linear energy stable and miximum pribciple preserving semi-implicit scheme for Allen–Cahn equation with double well potential. Commun Nonlinear Sci Numer Simulat 98:105766 MATH Google Scholar
Kim J, Lee S, Choi Y (2014) A conservative Allen–Cahn equation with a space-time dependent Lagrange multiplier. Int J Eng Sci 84:11–17 MathSciNetMATH Google Scholar
Jeong D, Kim J (2017) Conservative Allen–Cahn–Navier–Stokes systems for incompressible two-phase fluid flows. Comput Fluid 156:239–246 MathSciNetMATH Google Scholar
Lee HG (2016) High-order and mass conservative methods for the conservative Allen–Cahn equation. Comput Math Appl 72:620–631 MathSciNetMATH 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 MathSciNet Google Scholar
Joshi V, Jaiman RK (2018) An adaptive variational procedure for the conservative and positivity preserving Allen–Cahn phase-field model. J Comput Phys 366:478–504 MathSciNetMATH Google Scholar
Huang Z, Lin G, Ardenaki AM (2020) Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen–Cahn model. J Comput Phys 420:109718 MathSciNetMATH Google Scholar
Aihara S, Takaki T, Takada N (2019) Multi-phase-field modeling using a conservative Allen–Cahn equation for multiphase flow. Comput Fluid 178:141–151 MathSciNetMATH Google Scholar
Li J, Ju L, Cai Y, Feng X (2021) Unconditionally maximum bound principle preserving linear schemes for the conservative Allen–Cahn equation with nonlocal constraint. J Sci Comput 87:98 MathSciNetMATH Google Scholar
Jiang K, Ju L, Li J, Li X (2021) Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects. Numer Method Partial Differential Equ. https://doi.org/10.1002/num.22827
Zhang J, Yang X (2020) Unconditionally energy stable large time stepping method for the \(L^2\)-gradient flow based ternary phase-field model with precise nonlocal volume conservation. Comput Methods Appl Mech Eng 361:112743 MATH Google Scholar
Yang X (2021) Efficient, second-order in time, and energy stable scheme for a new hydrodynamically coupled three components volume-conserved Allen–Cahn phase-field model. Math Model Method Appl Sci 31(4):753–787 MathSciNetMATH Google Scholar
Liu Z, Li X (2021) A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system. J Comput Phys 447:110703 MathSciNetMATH Google Scholar
Deville MO, Fischer PF, Mund EH (2002) High-order methods for incompressible fluid flow. Cambridge University Press, Cambridge, p 9 MATH Google Scholar
Chen W, Liu Y, Wang C, Wise SM (2016) Convergence analysis of a fully discrete finite difference scheme for the Cahn–Hilliard–Hele–Shaw equation. Math Comput 85:2231–2257 MathSciNetMATH Google Scholar
Liu Y, Chen W, Wang C, Wise SM (2017) Error analysis of a mixed finite element method for a Cahn–Hilliard–Hele–Shaw system. Numer Math 135:679–709 MathSciNetMATH Google Scholar
Diegel AE, Wang C, Wang X, Wise SM (2017) Convergence analysis and error estimates for a second order accurate finite element method for the Cahn–Hilliard–Navier–Stokes system. Numer Math 137:495–534 MathSciNetMATH Google Scholar
Shen J, Xu J (2018) Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. SIAM J Numer Anal 56(5):2895–2912 MathSciNetMATH Google Scholar
Li X, Shen J, Rui H (2019) Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Math Comput 88:2047–2068 MathSciNetMATH Google Scholar
Wang M, Huang Q, Wang C (2021) A second order accurate scalar auxiliary variable (SAV) numerical method for the square phase field crystal equation. J Sci Comput 88:33 MathSciNetMATH Google Scholar
Huang F, Shen J (2021) Stability and error analysis of a class of high-order IMEX schemes for Navier–Stokes equations with periodic boundary conditions. SIAM J Numer Anal 59(6):2926–2954 MathSciNetMATH Google Scholar
Li X, Shen J (2020) On a SAV-MAC scheme for the Cahn–Hilliard–Navier-Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case. Math Model Meth Appl Sci 30(12):2263–2297 MathSciNetMATH Google Scholar
Trottenberg U, Oosterlee C, Schüller A (2001) Multigrid. Academic press, New York MATH Google Scholar
Shu CW, Osher S (1989) Efficient implementation of essentially non-oscillatory shock capturing schemes II. J Comput Phys 83:32–78 MathSciNetMATH Google Scholar
Bronsard L, Stoth B (1997) Volume-preserving mean curvature flow as a limit of a nonlocal Ginzburg–Landau equation. SIAM J Math Anal 28:769–807 MathSciNetMATH Google Scholar
Lee HG, Kim J (2012) A comparison study of the boussinesq and the variable density models on buoyancy-driven flows. J Eng Math 75:15–27 MathSciNetMATH Google Scholar
Zhu G, Kou J, Yao B, Wu YS, Yao J, Sun S (2019) Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants. J Fluid Mech 879:327–359 MathSciNetMATH 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 MathSciNet 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 MathSciNetMATH 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 MathSciNetMATH Google Scholar
Yang J, Kim J (2021) An efficient stabilized multiple auxiliary variables method for the Cahn–Hilliard–Darcy two-phase flow system. Comput Fluid 223:104948
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 Google Scholar
Yang J, Kim J (2021) Numerical study of the ternary Cahn–Hilliard fluids by using an efficient modified scalar auxiliary variable approach. Commun Nonlinear Sci Numer Simulat 102:105923 MathSciNetMATH Google Scholar