Journal of Applied and Computational Mechanics

Isogeometric Resolution of the Brinkman-Forchheimer-Darcy

Document Type : Research Paper

Authors

1 Department of Mathematics, MSISI, Laboratory, Faculty of Sciences and Techniques of Errachidia, Moulay Ismail University of Meknes, B.P 509 Boutalamine, Errachidia, Morocco

2 Mechanical Engineering Laboratory, Sidi Mohamed Ben Abdellah University, Faculty of Sciences and Techniques, B.P. 2202 Route Imouzzer, Fez, 30000, Morocco

3 Department of Mathematics Regional Centre for Professions of Education and Training (CREMF Fès-Meknès), Rue de Koweit 49, Ville Nouvelle, Fez, 30050, Morocco

4 Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transylvania University of Brasov, Brasov, 500036, B-dul Eroilor 29, Romania

5 Department of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, 500036, B-dul Eroilor 29, Romania

6 Academy of Romanian Scientists, Bucharest, 050045, Str. Ilfov, Nr. 3, Romania

Abstract

In this paper, we employ the finite element method based on non-uniform rational B-splines function approximation to solve the nonlinear Brinkman-Forcheimer-Darcy equation in a simply connected and bounded Lipschitz domain Ω. We provide both theoretical and numerical studies of the Dirichlet boundary problem. Utilizing a stream function formulation, we demonstrate the well-posedness of the weak form. Furthermore, we approximate the velocity and pressure fields by linearizing the nonlinear terms, resulting in an algebraic system. This Non-uniform rational B-splines method is more effective in terms of the exact representation of the geometry and the good approximation of the solution compared to the virtual element method. To validate the effectiveness of the non-uniform rational B-splines Finite Element Method, we conduct numerical simulations of fluid flow in porous media.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Journal of Applied and Computational Mechanics

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