Multi-phase-field modeling using a conservative Allen–Cahn equation for multiphase flow

Aihara, Shintaro; Takaki, Tomohiro; Tsuji, Naoki

doi:10.1016/j.compfluid.2018.08.023

Cited by 81 publications

(29 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Multi-phase and multi-material flows.A conservative Allen-Cahn equation for multiphase flows is simulated in Aihara, Takaki and Takada (2019). A compressible multiphase approach for viscoelastic fluids and solids with relaxation and elasticity was pursued in Rodriguez and Johnsen (2019).…”

Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

118

View full text Add to dashboard Cite

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

show abstract

Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

118

View full text Add to dashboard Cite

show abstract

“…It was taken the advantage of being able to adjust time step to multiscale temporal characteristic of the phase separation and coarsening process. The nonlocal AC model can be applied to multiphase models coupled with incompressible Navier-Stokes (NS) equations [20][21][22]. Specifically, under the framework of the LB method, Ren et al [20] incorporated the incompressible hydrodynamic equations with the conservative AC equation and provided an effective solution for binary flow modeling, which had been difficult due to the interface limitations and numerical dispersion.…”

Section: ∂φ(X T) ∂Tmentioning

confidence: 99%

“…Specifically, under the framework of the LB method, Ren et al [20] incorporated the incompressible hydrodynamic equations with the conservative AC equation and provided an effective solution for binary flow modeling, which had been difficult due to the interface limitations and numerical dispersion. Aihara et al [21] developed a new multiphase method using the conservative AC equation and showed the accurate evaluation in the movement of bubbles interacting with the liquid-liquid interface. Furthermore, Joshi and Jaiman [22] proposed a nonlinear adaptive variational method to solve the coupled AC and NS equations for fluid-fluid phase flows, which is formulated by the finite element approach.…”

Section: ∂φ(X T) ∂Tmentioning

confidence: 99%

An Explicit Hybrid Method for the Nonlocal Allen–Cahn Equation

et al. 2020

View full text Add to dashboard Cite

We extend the explicit hybrid numerical method for solving the Allen–Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.

show abstract

“…By using this method, many interfacial processes at mesoscopic scale can be numerically simulated, such as the domain boundary evolution of ferroelectric materials, [ 4–7 ] the grain boundary evolution of polycrystalline materials, [ 8–11 ] the phase boundary evolution of dendritic solidification, [ 12–15 ] and the multiphase flow simulation. [ 16–19 ] However, it is difficult to define the physical meaning of each term in the phase‐field equation, and the explicit velocity of the diffuse interfacial movement cannot be obtained directly. Although the perturbation analysis method [ 20–22 ] can mathematically reveal the dynamical properties of the diffuse interface, it cannot present the physical meaning of the implicit dynamical equation.…”

Section: Introductionmentioning

confidence: 99%

Explicit Dynamics of Diffuse Interface in Phase‐Field Model

Yang

Huang

Liu

et al. 2020

Advcd Theory and Sims

View full text Add to dashboard Cite

Interfaces play an important role during phase transition and interfacial chemical reactions. In this paper, three different methods are introduced to analyze the explicit dynamics of the diffuse interface by means of phase-field model, and these methods are based on three independent perspectives: non-dispersive propagation of the interfacial waveform, the flux density and sources/sinks analysis of continuity equation, and the moving interfacial coordinate transformation. These theoretical derivations not only present the relationship between the diffuse interfacial velocity and the effect of driving force and interfacial curvature, but also clarify the equivalent method between the phase-field dynamics and the sharp-interfacial dynamics, which reveals the physical meaning of the diffuse interfacial dynamical equation from different perspectives. The present study advances the understanding of the interfacial phase transition and provides theoretical insights for the phase-field model and numerical simulation.

show abstract

Multi-phase-field modeling using a conservative Allen–Cahn equation for multiphase flow

Cited by 81 publications

References 52 publications

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

An Explicit Hybrid Method for the Nonlocal Allen–Cahn Equation

Explicit Dynamics of Diffuse Interface in Phase‐Field Model

Contact Info

Product

Resources

About