Error analysis of a decoupled, linear and stable finite element method for Cahn–Hilliard–Navier–Stokes equations

Chen, Yaoyao; Huang, Yunqing; Yi, Nianyu

doi:10.1016/j.amc.2022.126928

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…The approximate solutions are solved by MATLAB software; in all experiments, Ω is divided by quasiuniform rectangle meshes. The results of the suggested algorithm will be compared with those obtained with the Lagrange basis in terms of three error norms [36,37]:…”

Section: Approximation Of Solutions With the C-bézier Basismentioning

confidence: 99%

Numerical Solutions of Second-Order Elliptic Equations with C-Bézier Basis

Sun,

Su,

Pang

2024

Axioms

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This article introduces a finite element method based on the C-Bézier basis function for second-order elliptic equations. The trial function of the finite element method is set up using a combination of C-Bézier tensor product bases. One advantage of the C-Bézier basis is that it has a free shape parameter, which makes geometric modeling more convenience and flexible. The performance of the C-Bézier basis is searched for by studying three test examples. The numerical results demonstrate that this method is able to provide more accurate numerical approximations than the classical Lagrange basis.

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Section: Approximation Of Solutions With the C-bézier Basismentioning

confidence: 99%

Numerical Solutions of Second-Order Elliptic Equations with C-Bézier Basis

Sun,

Su,

Pang

2024

Axioms

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show abstract

Property-preserving numerical approximation of a Cahn–Hilliard–Navier–Stokes model with variable density and degenerate mobility

Acosta-Soba,

Guillén-González,

Rodríguez-Galván

et al. 2025

Applied Numerical Mathematics

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A Correct Benchmark Problem of a Two-Dimensional Droplet Deformation in Simple Shear Flow

Yang

Kim

2022

Mathematics

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In this article, we numerically investigate a two-dimensional (2D) droplet deformation and breakup in simple shear flow using a phase-field model for two-phase fluid flows. The dominant driving force for a droplet breakup in simple shear flow is the three-dimensional (3D) phenomenon via surface tension force and Rayleigh instability, where a liquid cylinder of certain wavelengths is unstable against surface perturbation and breaks up into individual droplets to reduce the total surface energy. A 2D droplet breakup does not occur except in special cases because there is only one curvature direction of the droplet interface, which resists breakup. However, there have been many numerical simulation research works on the 2D droplet breakups in simple shear flow. This study demonstrates that the 2D droplet breakup phenomenon in simple shear flow is due to the lack of space resolution of the numerical grid.

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Error analysis of a decoupled, linear and stable finite element method for Cahn–Hilliard–Navier–Stokes equations

Cited by 3 publications

References 21 publications

Numerical Solutions of Second-Order Elliptic Equations with C-Bézier Basis

Numerical Solutions of Second-Order Elliptic Equations with C-Bézier Basis

Property-preserving numerical approximation of a Cahn–Hilliard–Navier–Stokes model with variable density and degenerate mobility

A Correct Benchmark Problem of a Two-Dimensional Droplet Deformation in Simple Shear Flow

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