The scalar auxiliary variable (SAV) approach for gradient flows
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Publication:1701293
DOI10.1016/j.jcp.2017.10.021zbMath1380.65181OpenAlexW2766149883MaRDI QIDQ1701293
Publication date: 22 February 2018
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2017.10.021
PDEs in connection with fluid mechanics (35Q35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)
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Cites Work
- On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations
- Finite element approximation of nematic liquid crystal flows using a saddle-point structure
- Exponential time differencing for stiff systems
- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- Epitaxial growth without slope selection: energetics, coarsening, and dynamic scaling
- Spectral deferred correction methods for ordinary differential equations
- Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
- Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
- Numerical approximations for a phase-field moving contact line model with variable densities and viscosities
- Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
- A novel linear second order unconditionally energy stable scheme for a hydrodynamic \(\mathbf{Q} \)-tensor model of liquid crystals
- Linear and unconditionally energy stable schemes for the binary fluid-surfactant phase field model
- On linear schemes for a Cahn-Hilliard diffuse interface model
- Long Time Numerical Simulations for Phase-Field Problems Using $p$-Adaptive Spectral Deferred Correction Methods
- The Global Dynamics of Discrete Semilinear Parabolic Equations
- Phase-Field Models for Multi-Component Fluid Flows
- A diffuse-interface method for simulating two-phase flows of complex fluids
- DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS
- TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
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