Second order linear decoupled energy dissipation rate preserving schemes for the Cahn-Hilliard-extended-Darcy model

Li, Yakun; Yu, Wenkai; Zhao, Jia; Wang, Qi

doi:10.1016/j.jcp.2021.110561

Cited by 5 publications

(4 citation statements)

References 57 publications

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Section: Numerical Experimentssupporting

confidence: 90%

“…From Figure 6, we can observe that the small viscous ratio accelerates the dynamical process and leads to more satellite drops after rupture. The numerical results are very consistent with those reported in [13, 27, 35, 46]. We also simulate the interface pinch‐off in three dimensions for binary fluids by setting the initial phase variable

{\xi}_{\pm}\left(x,y,z\right)=1\pm \tanh \left(\frac{4}{3\epsilon}\left(\sqrt{{\left(z-\frac{1}{3}\right)}^2+{\left(y-\frac{1}{3}\right)}^2}\pm \frac{1}{4\pi}\left(1+\frac{\cos \left(2\pi x\right)}{2}\right)\right)\right),

in computational domain

\left[0,1\right]\times \left[0,1\right]\times \left[0,1.5\right]

.…”

Section: Numerical Experimentssupporting

confidence: 81%

“…The CHD system is a strongly coupled nonlinear system that models interfacial phenomena with sharp transitions in narrow layers (stiffness). There have been abundant numerical works addressing these challenges [14,16,22,26,27,35,46,47]. Feng and Wise [14] analyzed a fully discrete implicit finite element method for studying the CHD system, establishing unconditional unique solvability and convergence of the numerical scheme.…”

Section: Introductionmentioning

confidence: 99%

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Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system

Gao,

Han

2024

Numerical Methods Partial

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We develop two totally decoupled, linear and second‐order accurate numerical methods that are unconditionally energy stable for solving the Cahn–Hilliard–Darcy equations for two phase flows in porous media or in a Hele‐Shaw cell. The implicit‐explicit Crank–Nicolson leapfrog method is employed for the discretization of the Cahn–Hiliard equation to obtain linear schemes. Furthermore the artificial compression technique and pressure correction methods are utilized, respectively, so that the Cahn–Hiliard equation and the update of the Darcy pressure can be solved independently. We establish unconditionally long time stability of the schemes. Ample numerical experiments are performed to demonstrate the accuracy and robustness of the numerical methods, including simulations of the Rayleigh–Taylor instability, the Saffman–Taylor instability (fingering phenomenon).

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Section: Numerical Experimentssupporting

confidence: 90%

{\xi}_{\pm}\left(x,y,z\right)=1\pm \tanh \left(\frac{4}{3\epsilon}\left(\sqrt{{\left(z-\frac{1}{3}\right)}^2+{\left(y-\frac{1}{3}\right)}^2}\pm \frac{1}{4\pi}\left(1+\frac{\cos \left(2\pi x\right)}{2}\right)\right)\right),

in computational domain

\left[0,1\right]\times \left[0,1\right]\times \left[0,1.5\right]

.…”

Section: Numerical Experimentssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system

Gao,

Han

2024

Numerical Methods Partial

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show abstract

“…Given any boundary conditions along ∂Ω, we need to check their consistence with the governing equation in Ω [23]. We integrate equation (2.5) over Ω to obtain…”

Section: Dirichlet Boundary-value Problemmentioning

confidence: 99%

Boundary-to-Solution Mapping for Groundwater Flows in a Toth Basin

Sun¹,

Li²,

Hao³

et al. 2023

Preprint

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In this paper, the authors propose a new approach to solving the groundwater flow equation in the Toth basin of arbitrary top and bottom topographies using deep learning. Instead of using traditional numerical solvers, they use a DeepONet to produce the boundary-to-solution mapping. This mapping takes the geometry of the physical domain along with the boundary conditions as inputs to output the steady state solution of the groundwater flow equation. To implement the DeepONet, the authors approximate the top and bottom boundaries using truncated Fourier series or piecewise linear representations. They present two different implementations of the DeepONet: one where the Toth basin is embedded in a rectangular computational domain, and another where the Toth basin with arbitrary top and bottom boundaries is mapped into a rectangular computational domain via a nonlinear transformation. They implement the Deep-ONet with respect to the Dirichlet and Robin boundary condition at the top and the Neumann boundary condition at the impervious bottom boundary, respectively. Using this deep-learning enabled tool, the authors investigate the impact of surface topography on the flow pattern by both the top surface and the bottom impervious boundary with arbitrary geometries. They discover that the average slope of the top surface promotes long-distance transport, while the local curvature controls localized circulations. Additionally, they find that the slope of the bottom impervious boundary can seriously impact the long-distance transport of groundwater flows. Overall, this paper presents a new and innovative approach to solving the groundwater flow equation using deep learning, which allows for the investigation of the impact of surface topography on groundwater flow patterns.

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A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system

Wang,

Zou,

2024

Adv Comput Math

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Second order linear decoupled energy dissipation rate preserving schemes for the Cahn-Hilliard-extended-Darcy model

Cited by 5 publications

References 57 publications

Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system

Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system

Boundary-to-Solution Mapping for Groundwater Flows in a Toth Basin

A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system

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