Diffuse interface model for incompressible two-phase flows with large density ratios

Ding, Hang; Spelt, Peter D. M.; Chen, Shu

doi:10.1016/j.jcp.2007.06.028

Cited by 601 publications

(551 citation statements)

References 31 publications

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“…We use a finite-volume approach similar to the one developed by Ding, Spelt & Shu (2007) in order to solve the system of equations (2.7)-(2.10). These equations are discretized using a staggered grid.…”

Section: Numerical Solution 31 Methodsmentioning

confidence: 99%

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Double diffusive effects on pressure-driven miscible displacement flows in a channel

2012

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The pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

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Section: Numerical Solution 31 Methodsmentioning

confidence: 99%

“…The numerical procedure described above was developed by Ding et al (2007) in the context of interfacial flows. Sahu et al (2009a,b) modified this finite-volume method to simulate pressure-driven neutrally buoyant miscible channel flow with high viscosity contrast.…”

Section: Numerical Solution 31 Methodsmentioning

confidence: 99%

Double diffusive effects on pressure-driven miscible displacement flows in a channel

2012

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“…Ding [10] and Boyer [5] each came up with alternative generalizations of Model H for different densities. Their starting point are the equations for the mass conservation of each phase…”

Section: Phase Field-based Two-phase Flow Modelsmentioning

confidence: 99%

Isogeometric Analysis of the Navier–Stokes–Cahn–Hilliard equations with application to incompressible two-phase flows

Hosseini

Turek

Möller

et al. 2017

Journal of Computational Physics

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In this work, we present our numerical results of the application of Galerkin-based Isogeometric Analysis (IGA) to incompressible Navier-Stokes-Cahn-Hilliard (NSCH) equations in velocity-pressurephase field-chemical potential formulation. For the approximation of the velocity and pressure fields, LBB compatible non-uniform rational B-spline spaces are used which can be regarded as smooth generalizations of Taylor-Hood pairs of finite element spaces. The one-step θ-scheme is used for the discretization in time. The static and rising bubble, in addition to the nonlinear Rayleigh-Taylor instability flow problems, are considered in two dimensions as model problems in order to investigate the numerical properties of the scheme.

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“…The last velocity interface boundary condition is exactly the Beavers-Joseph-SaffmanJones interface boundary condition [10,12,14,15,60,61,62,63,64,65] with the slip coefficient β equal to the Beavers-Joseph-Saffman-Jones coefficient α BJSJ . The Cahn-Hilliard-Stokes system can be viewed as the low Reynolds number approximation of the better-known Cahn-Hilliard-Navier-Stokes system for two phase flow [28,35,34,36,40,66,67,68,69,70]. The derivation above indicates that the interface boundary conditions (except for the three obtained via conservation of mass consideration) are in fact variational interface boundary conditions.…”

Section: Application Of Onsager's Extremum Principlementioning

confidence: 99%

Two‐phase flows in karstic geometry

Han

Sun

Wang

2013

Math Methods in App Sciences

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Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications.In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. Despite the importance of the subject, little work has been done on multi-phase flows in karstic geometry.In this paper we present a family of phase field (diffusive interface) models for two phase flow in karstic geometry. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws. Uniquely solvable first and second order in time numerical schemes that preserve the associated energy law are presented as well.

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Diffuse interface model for incompressible two-phase flows with large density ratios

Cited by 601 publications

References 31 publications

Double diffusive effects on pressure-driven miscible displacement flows in a channel

Double diffusive effects on pressure-driven miscible displacement flows in a channel

Isogeometric Analysis of the Navier–Stokes–Cahn–Hilliard equations with application to incompressible two-phase flows

Two‐phase flows in karstic geometry

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