A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities

Feng, Xiang; Kou, Jisheng; Sun, Shuyu

doi:10.1007/978-3-319-93713-7_9

Cited by 9 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Two main types of this model include the Allen-Cahn and Cahn-Hilliard equations. The governing equations for both types have been delineated and investigated in the literature 37,38 ; however, this article largely focuses on the Cahn-Hilliard equation, especially in conjunction with the Navier-Stokes equation [39][40][41] . On top of that, the Cahn-Hilliard equation has been successfully coupled with different viscoelastic fluid models in previous works [42][43][44] that investigate the applicability of the phase-field model to solve multi-phase non-Newtonian fluid flow.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of jet mode in electrospraying of Newtonian and viscoelastic fluids

Panahi

Pishevar

Tavakoli

2020

International Journal of Multiphase Flow

View full text Add to dashboard Cite

The purpose of this article is to explore the role of viscoelastic properties of polymeric solutions on the jet mode in the electrospray process. In this research, several numerical simulations were performed to model the behavior of electrified Newtonian and viscoelastic jets. First, used for validating viscoelastic constitutive equations and their implementation, the benchmark problem of the sedimenting sphere is stabilized beyond the previously suggested threshold. Then, an electrified DI water jet was simulated, and the obtained jet profile was compared with the experimental data from previous publications. Finally, the proposed algorithm was used to simulate viscoelastic electrified jets, where the effect of the Weissenberg number (Wi) on the jet profile was examined. In agreement with the previously obtained experimental results, by increasing the solution concentration, the asymptotic profile of the jet is reached at a smaller length from the nozzle, while the final thickness of the jet is slightly reduced.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical simulation of jet mode in electrospraying of Newtonian and viscoelastic fluids

Panahi

Pishevar

Tavakoli

2020

International Journal of Multiphase Flow

View full text Add to dashboard Cite

show abstract

“…Many authors have explored how to relax the incompressibility constraint ∇ · u = 0 in Navier-Stokes and Navier-Stokes/Cahn-Hilliard systems by using the artificial (or pseudo) compressibility method [6,27,28,29]. We use the time derivative of the pressure [27,25,9],…”

Section: Governing Equations Continuous Entropy Analysismentioning

confidence: 99%

“…where M = J a ξ , J a η , J a ζ . We use (28) to write the divergence of an entire block vector compactly. Thus, we define the block matrix M,…”

Section: Differential Geometry and Curvilinear Elementsmentioning

confidence: 99%

Entropy–stable discontinuous Galerkin approximation with summation–by–parts property for the incompressible Navier–Stokes/Cahn–Hilliard system

Manzanero

Rubio

Kopriva

et al. 2020

Journal of Computational Physics

View full text Add to dashboard Cite

We develop an entropy stable two-phase incompressible Navier-Stokes/Cahn-Hilliard discontinuous Galerkin (DG) flow solver method. The model poses the Cahn-Hilliard equation as the phase field method, a skew-symmetric form of the momentum equation, and an artificial compressibility method to compute the pressure. We design the model so that it satisfies an entropy law, including free-and no-slip wall boundary conditions with non-zero wall contact angle. We then construct a high-order DG approximation of the model that satisfies the SBP-SAT property. With the help of a discrete stability analysis, the scheme has two modes: an entropy conserving approximation with central advective fluxes and the Bassi-Rebay 1 (BR1) method for diffusion, and an entropy stable approximation with an exact Riemann solver for advection and interface stabilization added to the BR1 method. The scheme is applicable to, and the stability proofs hold for, three-dimensional unstructured meshes with curvilinear hexahedral elements. We test the convergence of the schemes on a manufactured solution, and their robustness by solving a flow initialized from random numbers. In the latter, we find that a similar scheme that does not satisfy an entropy inequality had 30% probability to fail, while the entropy stable scheme never does. We also solve the static and rising bubble test problems, and to challenge the solver capabilities we compute a three-dimensional pipe flow in the annular regime.

show abstract

“…Other methods like the molecular dynamics simulation [27,28] is also used to study solidification. The enthalpy-porosity method [29] and the phase field method [30,31,32] attracted a lot of research attention as the mesh-based methods. They not only circumvent the difficulties of interface reconstruction but also maintain the reproduction of physical properties.…”

Section: Introductionmentioning

confidence: 99%

Benchmark modeling and 3D applications of solidification and macro-segregation based on an operator-splitting and fully decoupled scheme with term-wise matrix assembly

Feng¹,

Chen²,

Sun³

2023

Preprint

View full text Add to dashboard Cite

Highlights• An operator-splitting and matrix-based scheme is proposed.• This fully decoupled scheme enhances implementability.• The mix of vectorization and forward matrix assembly benefits 3D applications.• A term-wise strategy is suggested to balance the computational costs and the complexity of implementation.• Plenty of benchmark cases validate the accuracy and efficiency of this method.

show abstract

A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities

Cited by 9 publications

References 26 publications

Numerical simulation of jet mode in electrospraying of Newtonian and viscoelastic fluids

Numerical simulation of jet mode in electrospraying of Newtonian and viscoelastic fluids

Entropy–stable discontinuous Galerkin approximation with summation–by–parts property for the incompressible Navier–Stokes/Cahn–Hilliard system

Benchmark modeling and 3D applications of solidification and macro-segregation based on an operator-splitting and fully decoupled scheme with term-wise matrix assembly

Contact Info

Product

Resources

About