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Flow of Newtonian Incompressible Fluids in Square Media: Isogeometric vs. Standard Finite Element Method

Author

Listed:
  • Maria Luminița Scutaru

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

  • Sohaib Guendaoui

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

  • Ouadie Koubaiti

    (MSISI Laboratory, Faculty of Sciences and Technics of Errachidia, Moulay Ismail University of Meknes, BP:298 Marjane 2, Meknes 50050, Morocco)

  • Lahcen El Ouadefli

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

Abstract

This article highlights a study focused on resolving a nonlinear problem in fluid dynamics using the Navier–Stokes equations as a mathematical model. The study focuses on comparing the isogeometric analysis (IGA) B-spline method with the traditional finite element method (FEM) in a two-dimensional context. The objective is to showcase the superior performance of the IGA method in terms of result quality and computational efficiency. The study employs GEOPDE’s MATLAB code for implementing and computing the NURBS method and COMSOL Software’s FEM code for comparison. The advantages of the IGA B-spline method are highlighted, including its ability to accurately capture complex flow behavior and its reduced computation time compared to FEM. The study aims to establish the superiority of the IGA method in solving nonlinear Navier–Stokes equations, providing valuable insights for fluid dynamics and practical implications for engineering simulations.

Suggested Citation

  • Maria Luminița Scutaru & Sohaib Guendaoui & Ouadie Koubaiti & Lahcen El Ouadefli & Abdeslam El Akkad & Ahmed Elkhalfi & Sorin Vlase, 2023. "Flow of Newtonian Incompressible Fluids in Square Media: Isogeometric vs. Standard Finite Element Method," Mathematics, MDPI, vol. 11(17), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3702-:d:1227184
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    References listed on IDEAS

    as
    1. Omar El Moutea & Lahcen El Ouadefli & Abdeslam El Akkad & Nadia Nakbi & Ahmed Elkhalfi & Maria Luminita Scutaru & Sorin Vlase, 2023. "A Posteriori Error Estimators for the Quasi-Newtonian Stokes Problem with a General Boundary Condition," Mathematics, MDPI, vol. 11(8), pages 1-20, April.
    2. Lahcen El Ouadefli & Abdeslam El Akkad & Omar El Moutea & Hassan Moustabchir & Ahmed Elkhalfi & Maria Luminița Scutaru & Radu Muntean, 2022. "Numerical Simulation for Brinkman System with Varied Permeability Tensor," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    3. 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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