A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations

Mohammed Louaked (1) , Nour Seloula (1) , Shuyu Sun , Saber Trabelsi (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 LJLL - Laboratoire Jacques-Louis Lions

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 externel forces. Next, we propose and study a perturbed compressible system that approximate the Brinkman-Forchheimer equations. Finally, we propose a time dicretization of the perturbed system by a semi-implicit Euler scheme and next a lowesst-order Raviart-Thomas element is applied for spatial discretization. Some numerical results are given.

Keywords: Brinkman-Forchheimer equations; Continuous Dependence; artificial compressibility; Stability

Domains: Mathematics [math]; Mathematics [math]; Analysis of PDEs [math.AP]; Mathematics [math]; Numerical Analysis [math.NA]

Mohammed Louaked, Nour Seloula, Shuyu Sun, Saber Trabelsi. A pseudocompressibility method for the incompressible Brinkman-Forchheimer equations. Differential and integral equations, 2015. ⟨hal-02343592⟩