Differential and Integral Equations

A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations

Mohammed Louaked, Nour Seloula, Shuyu Sun, and Saber Trabelsi

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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.

Article information

Source
Differential Integral Equations, Volume 28, Number 3/4 (2015), 361-382.

Dates
First available in Project Euclid: 4 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1423055233

Mathematical Reviews number (MathSciNet)
MR3306568

Zentralblatt MATH identifier
1340.35264

Subjects
Primary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35K55: Nonlinear parabolic equations 35Q35: PDEs in connection with fluid mechanics

Citation

Louaked, Mohammed; Seloula, Nour; Sun, Shuyu; Trabelsi, Saber. A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations. Differential Integral Equations 28 (2015), no. 3/4, 361--382. https://projecteuclid.org/euclid.die/1423055233


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