Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model

Dehghan, Mehdi; Gharibi, Zeinab

doi:10.1016/j.amc.2021.126487

Cited by 14 publications

(2 citation statements)

References 57 publications

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“…(cf. [28,36,36,29,31,32,11,25,27,12,21,13])), demonstrating their substantial potential as a formidable numerical method in scientific computing. The key distinction between WG methods and other existing finite element techniques lies in their utilization of weak derivatives and weak continuities in formulating numerical schemes based on conventional weak forms for the underlying PDE problems.…”

Section: Scopementioning

confidence: 99%

Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem

Gharibi

Dehghan

2021

Applied Numerical Mathematics

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Section: Scopementioning

confidence: 99%

Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem

Gharibi

Dehghan

2021

Applied Numerical Mathematics

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“…Dehghan and Gharibi (2022) presented and analyzed a weak Galerkin finite element method for the coupled Navier–Stokes/temperature (or Boussinesq) problems. A fully-discrete scheme, based on the weak Galerkin method in space and backward Euler method in time, was proposed in Dehghan and Gharibi (2021) for solving the Cahn-Hilliard-Navier-Stokes model. Sze and Liu (2010) devised the six-node hybrid-Trefftz triangular finite element models via a hybrid variational principle for Helmholtz problem.…”

Section: Introductionmentioning

confidence: 99%

Simulation of coupled elasticity problem with pressure equation: hydroelastic equation

Hooshyarfarzin,

Abbaszadeh,

Dehghan

2024

MMMS

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PurposeThe main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.Design/methodology/approach First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.FindingsNumerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.Originality/valueThis is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

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Conforming Virtual Element Methods for Sobolev Equations

Zhou

Zhao

2022

J Sci Comput

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Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model

Cited by 14 publications

References 57 publications

Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem

Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem

Simulation of coupled elasticity problem with pressure equation: hydroelastic equation

Conforming Virtual Element Methods for Sobolev Equations

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