Advected phase-field method for bounded solution of the Cahn–Hilliard Navier–Stokes equations

Dadvand, Abdolrahman; Bagheri, Milad; Samkhaniani, Nima; Marschall, Holger; Wörner, Martin

doi:10.1063/5.0048614

Cited by 16 publications

(3 citation statements)

References 99 publications

(102 reference statements)

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“…The term f s = Φ rc models the capillarity of the diffusive interfaces on the basis of the Korteweg stress tensor. [31] Note that (Equation (4a)) is a fourth-order non-linear parabolic partial differential equation with respect to c, which renders it challenging to solve numerically. [32] 2.2 | N-phase Cahn-Hilliard Navier-Stokes equations…”

Section: Two-phase Cahn-hilliard Navier-stokes Equationsmentioning

confidence: 99%

A unified finite volume framework for phase‐field simulations of an arbitrary number of fluid phases

et al. 2022

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While the phase-field methodology is widely adopted for simulating two-phase flows, the simulation of an arbitrary number (N ≥ 2) of fluid phases at physical fidelity is non-trivial and requires special attention concerning mathematical modelling, numerical discretization, and solution algorithm. We present our most recent work with a focus on validation for multiple immiscible, incompressible, and isothermal phases, enhancing further our library for diffuse interface phase-field interface capturing methods in OpenFOAM (FOAMextend 4.0/4.1). The phase-field method is an energetic variational formulation based on the work of Cahn and Hilliard where the interface is composed of a physical diffuse layer resembling realistic interfaces. The evolution of the phases is then governed by the minimization of the free energy of the system.The accuracy of the method is demonstrated for a number of test problems, including a floating liquid lens, bubble rise in two stratified layers, and drop impact onto thin liquid film.

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Section: Two-phase Cahn-hilliard Navier-stokes Equationsmentioning

confidence: 99%

A unified finite volume framework for phase‐field simulations of an arbitrary number of fluid phases

et al. 2022

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“…According to the law of mass conservation, the increase in mass per unit time of a fluid micro element is equal to the net mass flowing into the fluid micro element at the same time interval. Accordingly, the differential form of the mass conservation equation (also known as the continuity equation) can be obtained [5]:…”

Section: Mass Conservation Equationmentioning

confidence: 99%

Intelligent Control of Cabin Environment Using Computational Fluid Dynamics for Intelligent Manufacturing

Wang¹,

Zeng²

2022

Fluid Dynamics &Amp; Materials Processing

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An efficient and versatile intelligent algorithm is developed for the control of the cabin environment of wind power generators. The method can be used to monitor and solve wind power generation problems at the same time. It also provides several advantages with respect to other traditional methods which imply significant workload and maintenance personnel. The functional requirements of the intelligent control system are analyzed, and a control algorithm for the stepping motor is selected and evaluated. Through the comparative analysis of the active power and internal temperature curve for three kinds of output power of the prototype, it is proved that the environmental intelligent control system greatly improves the operation efficiency, solves typical problems in the ventilator room environment, and provides a solid theoretical basis for further research in this field.

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“…where u is the velocity, M φ is the mobility coefficient, µ φ is the chemical potential defined as the variational derivative of the energy functional with respect to φ [33],…”

Section: A Conservative Allen-cahn Equationmentioning

confidence: 99%

Discrete unified gas kinetic scheme for the conservative Allen-Cahn equation

Zhang¹,

Liu²,

Guo³

et al. 2022

Preprint

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In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from the flux evaluation with linear reconstruction in the previous DUGKS is analyzed. It is found that the calculated microflux across the cell interface is only the solution to the target kinetic equation with first order accuracy, which can result in an inaccurate CACE since the force term is involved or the first moment of the collision model has no conservation property. To correctly recover the kinetic equation up to the second order accuracy, the value of the distribution function that will propagate along the characteristic line with ending point at the cell interface is appropriated by the parabolic reconstruction instead of the linear reconstruction. To validate the accuracy of the present DUGKS for the CACE, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zaleska disk and the deformation of a circular interface, have been simulated. Numerical results show that the present DUGKS scheme is able to capture the interface with improved accuracy when compared with the previous DUGKS.

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Advected phase-field method for bounded solution of the Cahn–Hilliard Navier–Stokes equations

Cited by 16 publications

References 99 publications

A unified finite volume framework for phase‐field simulations of an arbitrary number of fluid phases

A unified finite volume framework for phase‐field simulations of an arbitrary number of fluid phases

Intelligent Control of Cabin Environment Using Computational Fluid Dynamics for Intelligent Manufacturing

Discrete unified gas kinetic scheme for the conservative Allen-Cahn equation

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