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Mixed Isogeometric Analysis of the Brinkman Equation

Author

Listed:
  • Lahcen El Ouadefli

    (Mechanical Engineering Laboratory, Faculty of Sciences and Techniques, B.P. 2202 Route Imouzzer, Fes 30000, Morocco)

  • Omar El Moutea

    (Laboratory of Mathematics and Applications ENS, Hassan II University Casablanca, Casablanca 20000, Morocco)

  • Abdeslam El Akkad

    (Mechanical Engineering Laboratory, Faculty of Sciences and Techniques, B.P. 2202 Route Imouzzer, Fes 30000, Morocco
    Département de Mathématiques, Centre Régional des Métiers d’Education et de Formation de Fès Meknès (CRMEF Fès-Meknès), Rue de Koweit 49, Ville Nouvelle, Fez 30050, Morocco)

  • Ahmed Elkhalfi

    (Mechanical Engineering Laboratory, Faculty of Sciences and Techniques, B.P. 2202 Route Imouzzer, Fes 30000, Morocco)

  • Sorin Vlase

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

  • Maria Luminița Scutaru

    (Faculty of Mechanical Engineering, Transilvania University of Brasov, 500019 Brașov, Romania)

Abstract

This study focuses on numerical solution to the Brinkman equation with mixed Dirichlet–Neumann boundary conditions utilizing isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS) within the Galerkin method framework. The authors suggest using different choices of compatible NURBS spaces, which may be considered a generalization of traditional finite element spaces for velocity and pressure approximation. In order to investigate the numerical properties of the suggested elements, two numerical experiments based on a square and a quarter of an annulus are discussed. The preliminary results for the Stokes problem are presented in References.

Suggested Citation

  • Lahcen El Ouadefli & Omar El Moutea & Abdeslam El Akkad & Ahmed Elkhalfi & Sorin Vlase & Maria Luminița Scutaru, 2023. "Mixed Isogeometric Analysis of the Brinkman Equation," Mathematics, MDPI, vol. 11(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2750-:d:1173407
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    References listed on IDEAS

    as
    1. Khadija Yakoubi & Soufiane Montassir & Hassane Moustabchir & Ahmed Elkhalfi & Catalin Iulian Pruncu & Jamal Arbaoui & Muhammad Umar Farooq, 2021. "An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure," Mathematics, MDPI, vol. 9(5), pages 1-10, March.
    2. Hosseini, Babak S. & Möller, Matthias & Turek, Stefan, 2015. "Isogeometric Analysis of the Navier–Stokes equations with Taylor–Hood B-spline elements," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 264-281.
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    Cited by:

    1. Khadija Yakoubi & Ahmed Elkhalfi & Hassane Moustabchir & Abdeslam El Akkad & Maria Luminita Scutaru & Sorin Vlase, 2023. "An Isogeometric Over-Deterministic Method (IG-ODM) to Determine Elastic Stress Intensity Factor (SIF) and T-Stress," Mathematics, MDPI, vol. 11(20), pages 1-12, October.

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