A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations

Mohammed Louaked; Nour Seloula; Shuyu Sun; Saber Trabelsi

A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations

Mohammed Louaked, Nour Seloula, Shuyu Sun, Saber Trabelsi

Research output: Contribution to journal › Article › peer-review

Abstract

In this work, we study the Brinkman-Forchheimer equations for unsteady flows. We prove the continuous dependence of the solution on the Brinkman’s and Forchheimer’s coefficients as well as the initial data and external forces. Next, we propose and study a perturbed compressible system that approximate the Brinkman-Forchheimer equations. Finally, we propose a time discretization of the perturbed system by a semi-implicit Euler scheme and next a lowest-order Raviart-Thomas element is applied for spatial discretization. Some numerical results are given.

Original language	English (US)
Journal	Differential and Integral Equations
State	Published - Jan 1 2016

Bibliographical note

KAUST Repository Item: Exported on 2021-02-21
Acknowledgements: The research of S. Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.
The authors warmly acknowledge Amgad Salama for valuable comments and discussions and his suggestions concerning the numerical part.

Cite this

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title = "A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations",

abstract = "In this work, we study the Brinkman-Forchheimer equations for unsteady flows. We prove the continuous dependence of the solution on the Brinkman{\textquoteright}s and Forchheimer{\textquoteright}s coefficients as well as the initial data and external forces. Next, we propose and study a perturbed compressible system that approximate the Brinkman-Forchheimer equations. Finally, we propose a time discretization of the perturbed system by a semi-implicit Euler scheme and next a lowest-order Raviart-Thomas element is applied for spatial discretization. Some numerical results are given.",

author = "Mohammed Louaked and Nour Seloula and Shuyu Sun and Saber Trabelsi",

note = "KAUST Repository Item: Exported on 2021-02-21 Acknowledgements: The research of S. Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology. The authors warmly acknowledge Amgad Salama for valuable comments and discussions and his suggestions concerning the numerical part.",

year = "2016",

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language = "English (US)",

journal = "Differential and Integral Equations",

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T1 - A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations

AU - Louaked, Mohammed

AU - Seloula, Nour

AU - Sun, Shuyu

AU - Trabelsi, Saber

N1 - KAUST Repository Item: Exported on 2021-02-21 Acknowledgements: The research of S. Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology. The authors warmly acknowledge Amgad Salama for valuable comments and discussions and his suggestions concerning the numerical part.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this work, we study the Brinkman-Forchheimer equations for unsteady flows. We prove the continuous dependence of the solution on the Brinkman’s and Forchheimer’s coefficients as well as the initial data and external forces. Next, we propose and study a perturbed compressible system that approximate the Brinkman-Forchheimer equations. Finally, we propose a time discretization of the perturbed system by a semi-implicit Euler scheme and next a lowest-order Raviart-Thomas element is applied for spatial discretization. Some numerical results are given.

AB - In this work, we study the Brinkman-Forchheimer equations for unsteady flows. We prove the continuous dependence of the solution on the Brinkman’s and Forchheimer’s coefficients as well as the initial data and external forces. Next, we propose and study a perturbed compressible system that approximate the Brinkman-Forchheimer equations. Finally, we propose a time discretization of the perturbed system by a semi-implicit Euler scheme and next a lowest-order Raviart-Thomas element is applied for spatial discretization. Some numerical results are given.

UR - http://hdl.handle.net/10754/662442

UR - https://projecteuclid.org/euclid.die/1423055233

M3 - Article

SN - 0893-4983

JO - Differential and Integral Equations

JF - Differential and Integral Equations

ER -

A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations

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