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Power law slip boundary condition for Navier-Stokes equations: Discontinuous Galerkin schemes

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Abstract

This study deals with the numerical analysis of several discontinuous Galerkin (DG) methods for the resolution of the Navier-Stokes equations with power law slip boundary condition. The physical context corresponding to this problem is the description of a flow when a position and the direction slip boundary condition is taken into consideration. The main goal in this work is to examine the solvability, convergence of several DG methods, and to discuss their practical resolution by means of fixed point iterative algorithm. Theoretical findings are backed up by solid computational results.

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Acknowledgements

The authors thank the two referees for their constructive remarks and comments.

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Authors and Affiliations

  1. African Peer Review Mechanism, Johannesburg, South Africa

    J. K. Djoko

  2. School of Mathematical and Statistical Sciences, North West University, Potchefstroom, South Africa

    J. K. Djoko

  3. University of Johannesburg, College of Business and Economics, Finance and Investment Management, Johannesburg, South Africa

    V. S. Konlack

  4. Laboratoire de Mathematiques et Applications, Unite de recherche Mathematiques et Modelisation, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beirut, 1107 2050, Lebanon

    T. Sayah

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  1. J. K. Djoko
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  2. V. S. Konlack
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  3. T. Sayah
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Djoko, J.K., Konlack, V.S. & Sayah, T. Power law slip boundary condition for Navier-Stokes equations: Discontinuous Galerkin schemes. Comput Geosci 28, 107–127 (2024). https://doi.org/10.1007/s10596-023-10265-8

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