A posteriori error analysis for Navier–Stokes equations coupled with Darcy problem

Hadji, M. L.; Assala, A.; Nouri, F. Z.

doi:10.1007/s10092-014-0130-z

Cited by 7 publications

(3 citation statements)

References 12 publications

(15 reference statements)

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“…This is an alternative to [28], where two Cahn-Hilliard equations are solved on Ω m and Ω c separately. The other three interface conditions (2.11)-(2.13) are utilized in the traditional way for the single-phase Navier-Stokes-Darcy model in the literature [40,29,35].…”

Section: The Weak Formulationmentioning

confidence: 99%

A decoupled numerical method for two-phase flows of different densities and viscosities in superposed fluid and porous layers

Gao¹,

Han²,

He³

et al. 2021

Preprint

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In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are coupled by seven domain interface boundary conditions. We show that the coupled model satisfies an energy law. Based on the ideas of pressure stabilization and artificial compressibility, we propose an unconditionally stable time stepping method that decouples the computation of the phase field variable, the velocity and pressure of free flow, the velocity and pressure of porous media, hence significantly reduces the computational cost. The energy stability of the scheme effected with the finite element spatial discretization is rigorously established. We verify numerically that our schemes are convergent and energy-law preserving. Ample numerical experiments are performed to illustrate the features of two-phase flows in the coupled free flow and porous media setting.

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Section: The Weak Formulationmentioning

confidence: 99%

A decoupled numerical method for two-phase flows of different densities and viscosities in superposed fluid and porous layers

Gao¹,

Han²,

He³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…However, only few works exist for the coupled Navier-Stokes/Darcy problem, see for instance [11,24]. Up to the author's knowledge, the first work dealing with adaptive algorithms for the Navier-Stokes/Darcy coupling is [24], where an a posteriori error estimator for a discontinuous Galerkin approximation of this coupled problem with constant parameters is proposed. In [11], the authors have derived a reliable and efficient residual-based a posteriori error estimator for the three dimensional version of the augmented-mixed method introduced in [12].…”

Section: Introductionmentioning

confidence: 99%

Residual-Based a Posteriori Error Estimates for a Conforming Finite Element Discretization of the Navier-Stokes/Darcy Coupled Problem

Houédanou¹,

Adetola²,

Ahounou³

2017

Jour. Pure Appl. Math. Adv. Appl.

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We consider in this paper, a new a posteriori residual type error estimator of a conforming mixed finite element method for the coupling of fluid flow with porous media flow on isotropic meshes. Flows are governed by the Navier-Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-JosephSaffman law. The finite element subspaces consider Bernardi-Raugel and Raviart- KOFFI WILFRID HOUEDANOU et al. 38 Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for a Lagrange multiplier defined on the interface. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. In addition, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

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A multilevel decoupling method for the Navier–Stokes/Darcy model

Chidyagwai

2017

Journal of Computational and Applied Mathematics

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A posteriori error analysis for Navier–Stokes equations coupled with Darcy problem

Cited by 7 publications

References 12 publications

A decoupled numerical method for two-phase flows of different densities and viscosities in superposed fluid and porous layers

A decoupled numerical method for two-phase flows of different densities and viscosities in superposed fluid and porous layers

Residual-Based a Posteriori Error Estimates for a Conforming Finite Element Discretization of the Navier-Stokes/Darcy Coupled Problem

A multilevel decoupling method for the Navier–Stokes/Darcy model

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