A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

Handle URI:
http://hdl.handle.net/10754/623504
Title:
A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios
Authors:
Xie, Yu; Wodo, Olga; Ganapathysubramanian, Baskar
Abstract:
In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.
Citation:
Xie Y, Wodo O, Ganapathysubramanian B (2016) A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios. Modeling and Simulation in Science, Engineering and Technology: 203–215. Available: http://dx.doi.org/10.1007/978-3-319-40827-9_16.
Publisher:
Springer Nature
Journal:
Advances in Computational Fluid-Structure Interaction and Flow Simulation
Issue Date:
4-Oct-2016
DOI:
10.1007/978-3-319-40827-9_16
Type:
Book Chapter
ISSN:
2164-3679; 2164-3725
Sponsors:
The authors acknowledge partial funding from KAUST CRG, NSF 1236839, and NSF 1149365. Computing support from NSF XSEDE via TG-CTS110007 is gratefully acknowledged.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorXie, Yuen
dc.contributor.authorWodo, Olgaen
dc.contributor.authorGanapathysubramanian, Baskaren
dc.date.accessioned2017-05-15T10:35:05Z-
dc.date.available2017-05-15T10:35:05Z-
dc.date.issued2016-10-04en
dc.identifier.citationXie Y, Wodo O, Ganapathysubramanian B (2016) A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios. Modeling and Simulation in Science, Engineering and Technology: 203–215. Available: http://dx.doi.org/10.1007/978-3-319-40827-9_16.en
dc.identifier.issn2164-3679en
dc.identifier.issn2164-3725en
dc.identifier.doi10.1007/978-3-319-40827-9_16en
dc.identifier.urihttp://hdl.handle.net/10754/623504-
dc.description.abstractIn this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.en
dc.description.sponsorshipThe authors acknowledge partial funding from KAUST CRG, NSF 1236839, and NSF 1149365. Computing support from NSF XSEDE via TG-CTS110007 is gratefully acknowledged.en
dc.publisherSpringer Natureen
dc.titleA Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratiosen
dc.typeBook Chapteren
dc.identifier.journalAdvances in Computational Fluid-Structure Interaction and Flow Simulationen
dc.contributor.institutionDepartment of Mechanical Engineering, Iowa State University, Ames, IA, USAen
dc.contributor.institutionMaterials Design and Innovation Department, Mechanical and Aerospace Department, University at Buffalo, Buffalo, NY, USAen
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