A new Allen-Cahn type two-model phase-field crystal model for fcc ordering and its numerical approximation

DOI10.1016/j.aml.2022.108211OpenAlexW4281976037WikidataQ114210479 ScholiaQ114210479MaRDI QIDQ2673754

Yanyan Li

Publication date: 13 June 2022

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2022.108211

zbMATH Keywords

energy stabilityconserved Allen-Cahnface-centered-cubictwo model phase-field crystal

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Initial-boundary value problems for higher-order parabolic equations (35K35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (7)

Modified multi-phase diffuse-interface model for compound droplets in contact with solid ⋮ Numerical simulation for the conserved Allen-Cahn phase field model of two-phase incompressible flows by an efficient dimension splitting method ⋮ Unconditionally energy-stable linear convex splitting algorithm for the \(L^2\) quasicrystals ⋮ A Second-Order, Linear, \(\boldsymbol{L^\infty}\)-Convergent, and Energy Stable Scheme for the Phase Field Crystal Equation ⋮ A second order accurate SAV numerical method for the nonlocal ternary conservative Allen-Cahn model ⋮ Linear energy-stable method with correction technique for the Ohta-Kawasaki-Navier-Stokes model of incompressible diblock copolymer melt ⋮ Generalized Allen-Cahn-type phase-field crystal model with FCC ordering structure and its conservative high-order accurate algorithm

Cites Work

• Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
• Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
• Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation
• Generalized SAV approaches for gradient systems
• Numerical approximation of the two-component PFC models for binary colloidal crystals: efficient, decoupled, and second-order unconditionally energy stable schemes
• The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes
• A high-order and unconditionally energy stable scheme for the conservative Allen-Cahn equation with a nonlocal Lagrange multiplier
• A second-order BDF scheme for the Swift-Hohenberg gradient flows with quadratic-cubic nonlinearity and vacancy potential
• A novel fully-decoupled, second-order time-accurate, unconditionally energy stable scheme for a flow-coupled volume-conserved phase-field elastic bending energy model
• A new Lagrange multiplier approach for gradient flows
• Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction
• On efficient numerical schemes for a two-mode phase field crystal model with face-centered-cubic (FCC) ordering structure
• A new conservative Swift-Hohenberg equation and its mass conservative method
• Numerical approximations for a new \(L^2\)-gradient flow based phase field crystal model with precise nonlocal mass conservation
• Nonlocal reaction—diffusion equations and nucleation
• A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
• Pattern formation outside of equilibrium

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