A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio

Wang, Yan; Chen, Shu; Shao, J. Y.; Wu, Jie; Niu, Xiaodong

doi:10.1016/j.jcp.2015.03.005

Cited by 97 publications

(50 citation statements)

References 35 publications

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“…Due to appearance of the diffusion term and numerical dissipation introduced in discretization of the convective term in the Cahn-Hilliard equation, the total mass of the binary fluid is usually not preserved exactly. This phenomenon has been reported in several works [47,53], where the phase-field models were used to study the binary incompressible fluid. The mass loss can get even worse for binary fluid flows with large density ratios, as large numerical dissipation is needed to obtain a stable solution.…”

Section: Introductionsupporting

confidence: 60%

“…To handle the issue of mass loss, usually the fine grids and small thickness of diffuse-interfaces are used in the phase-field model to improve mass conservation [3,12]. Another way to compensate the mass loss is to add the extra mass correction terms into the CH equation [47]. However, this may need additional efforts for correcting the order parameter at each time step, and the energy stability of the numerical methods can be hardly maintained due to the artificial mass correction term.…”

Section: Introductionmentioning

confidence: 99%

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Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier–Stokes–Cahn–Hilliard system: Primitive variable and projection-type schemes

Guo

Lin

Lowengrub

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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In this paper we describe two fully mass conservative, energy stable, finite difference methods on a staggered grid for the quasi-incompressible Navier-Stokes-Cahn-Hilliard (q-NSCH) system governing a binary incompressible fluid flow with variable density and viscosity. Both methods, namely the primitive method (finite difference method in the primitive variable formulation) and the projection method (finite difference method in a projection-type formulation), are so designed that the mass of the binary fluid is preserved, and the energy of the system equations is always non-increasing in time at the fully discrete level. We also present an efficient, practical nonlinear multigrid method -comprised of a standard FAS method for the Cahn-Hilliard equation, and a method based on the Vanka-type smoothing strategy for the Navier-Stokes equation -for solving these equations. We test the scheme in the context of Capillary Waves, rising droplets and Rayleigh-Taylor instability. Quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes. Moreover, in all cases, mass of the single component and the binary fluid was conserved up to 10 −8 and energy decreases in time.

show abstract

Section: Introductionsupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier–Stokes–Cahn–Hilliard system: Primitive variable and projection-type schemes

Guo

Lin

Lowengrub

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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show abstract

“…Wang et al proposed a multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio and high Reynolds number [22,23].…”

Section: Introductionmentioning

confidence: 99%

Chemical-potential-based lattice Boltzmann method for nonideal fluids

Wen

Zhou

et al. 2017

Phys. Rev. E

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“…In [21], a massconserved diffuse interface method is proposed for simulating incompressible flows of binary fluids with large density ratio. Aland [22] presented time integration for diffuse interface models for twophase flow.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation for multi-phase fluids considering different densities with continuous finite element method

Jiang

Yang

2018

J. Phys.: Conf. Ser.

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Abstract. In this paper, we compute a phase field model of Cahn-Hilliard type for multicomponent mixture fluids considering surface tension and buoyancy effects. We discretize Navier-Stokes and Cahn-Hilliard coupled equations with a continuous finite element scheme in space and the finite difference in time. Also, we apply a penalty formulation to the continuity equation which may increase the stability in solving the continuity condition and momentum equation. The dynamic of a rising lighter drop due to different densities between other two immiscible fluids is studied as the numerical example with a relatively coarse grid. Numerical results show that this model can be solved with a relative simple scheme and coarse grid which leads to the higher efficiency.

show abstract

A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio

Cited by 97 publications

References 35 publications

Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier–Stokes–Cahn–Hilliard system: Primitive variable and projection-type schemes

Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier–Stokes–Cahn–Hilliard system: Primitive variable and projection-type schemes

Chemical-potential-based lattice Boltzmann method for nonideal fluids

Numerical simulation for multi-phase fluids considering different densities with continuous finite element method

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