A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn–Hilliard–Navier–Stokes equation

Han, Daozhi; Wang, Xiaoming

doi:10.1016/j.jcp.2015.02.046

Cited by 184 publications

(103 citation statements)

References 37 publications

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“…a These schemes have been extended to NSCH systems with matched densities 31,39 and for quasiincompressible NSCH systems with a solenoidal mixture-velocity field. 15,22,44,47,48 However, non-solenoidal quasi-incompressible NSCH systems have only received scant consideration so far.…”

Section: Lowengrub and Truskinovskymentioning

confidence: 99%

Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

Roudbari

Şimşek

Brummelen

et al. 2018

Math. Models Methods Appl. Sci.

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While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier-Stokes Cahn-Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman-Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with nonsolenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and break-up dynamics of droplets including pinching due to gravity.

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Section: Lowengrub and Truskinovskymentioning

confidence: 99%

Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

Roudbari

Şimşek

Brummelen

et al. 2018

Math. Models Methods Appl. Sci.

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show abstract

“…It is highly desirable to have a second-order-in-time scheme, which inherits all essential advantages of the first-order schemes, to match accuracy of the second-order-in-space finite-difference method. Very recently, Han and Wang [13] developed a second order in time numerical scheme for Cahn-Hilliard-Navier-Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation.…”

Section: Second-order Schemementioning

confidence: 99%

Efficient, adaptive energy stable schemes for the incompressible Cahn–Hilliard Navier–Stokes phase-field models

Chen

Shen

2016

Journal of Computational Physics

105

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In this paper we develop a fully adaptive energy stable scheme for Cahn-Hilliard NavierStokes system, which is a phase-field model for two-phase incompressible flows, consisting a Cahn-Hilliard-type diffusion equation and a Navier-Stokes equation. This scheme, which is decoupled and unconditionally energy stable based on stabilization, involves adaptive mesh, adaptive time and a nonlinear multigrid finite difference method. Numerical experiments are carried out to validate the scheme for problems with matched density and non-matched density, and also demonstrate that CPU time can be significantly reduced with our adaptive approach.

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“…Remark 3.4 It is often desired to reach more than the first order accuracy in time. For the Navier-Stokes-Cahn-Hilliard system without moving contact lines a nonlinear energy stable second-order scheme has been proposed in [27]. However, it seems challenging to define a linear, energy stable, second-order scheme for the moving contact line problem.…”

Section: Remark 33mentioning

confidence: 99%

An efficient and energy stable scheme for a phase‐field model for the moving contact line problem

Aland

Chen

2015

Numerical Methods in Fluids

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SUMMARYIn this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier-StokesCahn-Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing property of the discrete energy, and demonstrate the effectiveness of our method through numerical simulations in both 2-D and 3-D. Copyright

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A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn–Hilliard–Navier–Stokes equation

Cited by 184 publications

References 37 publications

Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

Efficient, adaptive energy stable schemes for the incompressible Cahn–Hilliard Navier–Stokes phase-field models

An efficient and energy stable scheme for a phase‐field model for the moving contact line problem

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