A spectral element-based phase field method for incompressible two-phase flows Article Swipe
Yao Xiao
,
Zhong Zeng
,
Liangqi Zhang
,
Jingzhu Wang
,
Yiwei Wang
,
Hao Liu
,
Chenguang Huang
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1063/5.0077372
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1063/5.0077372
In this paper, we propose a spectral element-based phase field method by solving the Navier–Stokes/Cahn–Hilliard equations for incompressible two-phase flows. The high-order differential nonlinear term of the Cahn–Hilliard equation poses a great challenge for obtaining numerical solutions, so the Newton–Raphson method is adopted to tackle this conundrum. Furthermore, we employ the time-stepping scheme to decouple the Navier–Stokes equations to favor the computations with large density and viscosity contrast, in terms of both stability and convergence efficiency. In addition, the continuum surface tension model is used to account for the tangential component of the interfacial force, and thus our numerical method has the ability to simulate thermocapillary flows. We present four examples to demonstrate the interface capture accuracy of the proposed method. The shape of the rotating Zalesak's disk is accurately preserved by the present method even for two periods, which implies less dissipation and higher accuracy at long time numerical simulation. It is also noted that the present method with fourth-order element can achieve similar accuracy with the consistent scheme by evaluating the convective fluxes with the fifth-order weighted essentially non-oscillatory scheme. Moreover, the proposed method appears to comply well with mass conservation. And the results of thermocapillary flow test show good agreement with theoretical prediction. Finally, the rising bubble and Rayleigh–Taylor instability are considered to verify the proposed method for complex changes in interfacial topology, as well as its performance under large density and viscosity contrasts and high Reynolds number conditions.
Related Topics
Concepts
Physics
Mechanics
Rayleigh–Taylor instability
Cahn–Hilliard equation
Spectral method
Compressibility
Spectral element method
Numerical diffusion
Reynolds number
Classical mechanics
Incompressible flow
Nonlinear system
Navier–Stokes equations
Finite element method
Mathematical analysis
Instability
Partial differential equation
Extended finite element method
Mathematics
Thermodynamics
Turbulence
Quantum mechanics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1063/5.0077372
- https://aip.scitation.org/doi/pdf/10.1063/5.0077372
- OA Status
- bronze
- Cited By
- 16
- References
- 59
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4213281190
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4213281190Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1063/5.0077372Digital Object Identifier
- Title
-
A spectral element-based phase field method for incompressible two-phase flowsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-02-01Full publication date if available
- Authors
-
Yao Xiao, Zhong Zeng, Liangqi Zhang, Jingzhu Wang, Yiwei Wang, Hao Liu, Chenguang HuangList of authors in order
- Landing page
-
https://doi.org/10.1063/5.0077372Publisher landing page
- PDF URL
-
https://aip.scitation.org/doi/pdf/10.1063/5.0077372Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
bronzeOpen access status per OpenAlex
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https://aip.scitation.org/doi/pdf/10.1063/5.0077372Direct OA link when available
- Concepts
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Physics, Mechanics, Rayleigh–Taylor instability, Cahn–Hilliard equation, Spectral method, Compressibility, Spectral element method, Numerical diffusion, Reynolds number, Classical mechanics, Incompressible flow, Nonlinear system, Navier–Stokes equations, Finite element method, Mathematical analysis, Instability, Partial differential equation, Extended finite element method, Mathematics, Thermodynamics, Turbulence, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
16Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 4, 2024: 4, 2023: 6, 2022: 2Per-year citation counts (last 5 years)
- References (count)
-
59Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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