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A Novel Numerical Approach for Simulating the Nonlinear MHD Jeffery–Hamel Flow Problem

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Abstract

The present study is related to the numerical simulation of the well-known Jeffery Hamel blood flow problem of nonlinear form. For the numerical solutions of the designed model, a Bernoulli collocation method is implemented. The method is based on converting the model into a system of a nonlinear algebraic equation which is then solved using a novel iterative technique. To check the perfection and exactness of the proposed schemes, two novel residual error correction methods are illustrated to ensure that the method is effective. The method does not require any extensive computational time while providing good results. Some numerical simulations are provided and a comparison is made with other existing methods from the literature. From these results, it can be seen that the Bernoulli collocation method is effective yet simple in providing accurate results for such a model. The method can be extended in the near future for solving similar other problems with applications in both science and engineering.

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Acknowledgments

The authors would like to thank the referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura, Egypt

    Waleed Adel

  2. Department of Mathematics, Faculty of Arts and Sciences, Celal Bayar University, Muradiye Campus, Muradiye, 45047, Manisa, Turkey

    Kübra Erdem Biçer

  3. Department of Mathematics, Faculty of Science, Manisa Celal Bayar University, 45140, Manisa, Turkey

    Mehmet Sezer

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  1. Waleed Adel
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  2. Kübra Erdem Biçer
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  3. Mehmet Sezer
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Correspondence to Waleed Adel.

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Adel, W., Biçer, K.E. & Sezer, M. A Novel Numerical Approach for Simulating the Nonlinear MHD Jeffery–Hamel Flow Problem. Int. J. Appl. Comput. Math 7, 74 (2021). https://doi.org/10.1007/s40819-021-01016-3

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