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.
|Differential and Integral Equations
|Published - Jan 1 2016
Bibliographical noteKAUST 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.