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An Enhanced Finite Element Algorithm for Thermal Darcy Flows with Variable Viscosity

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Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12747))

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Abstract

This paper deals with the development of a stable and efficient unified finite element method for the numerical solution of thermal Darcy flows with variable viscosity. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields to a convection-diffusion equation for the heat transfer. The viscosity in the Darcy flows is assumed to be nonlinear depending on the temperature of the medium. The proposed method is based on combining a semi-Lagrangian scheme with a Galerkin finite element discretization of the governing equations along with an robust iterative solver for the associate linear systems. The main features of the enhanced finite element algorithm are that the same finite element space is used for all solutions to the problem including the pressure, velocity and temperature. In addition, the convection terms are accurately dealt with using the semi-Lagrangian scheme and the standard Courant-Friedrichs-Lewy condition is relaxed and the time truncation errors are reduced in the diffusion terms. Numerical results are presented for two examples to demonstrate the performance of the proposed finite element algorithm.

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Author information

Authors and Affiliations

  1. Laboratory Modeling Simulation and Data Analysis, University Mohammed VI Polytechnic, Benguerir, Morocco

    Loubna Salhi

  2. Mathematics and Applications Laboratory, FST, Abdelmalek Essaadi University, Tangier, Morocco

    Mofdi El-Amrani

  3. Department of Engineering, University of Durham, South Road, Durham, DH1 3LE, UK

    Mohammed Seaid

  4. International Water Research Institute, University Mohammed VI Polytechnic, Benguerir, Morocco

    Mohammed Seaid

Authors
  1. Loubna Salhi
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  2. Mofdi El-Amrani
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  3. Mohammed Seaid
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Corresponding author

Correspondence to Loubna Salhi .

Editor information

Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

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Salhi, L., El-Amrani, M., Seaid, M. (2021). An Enhanced Finite Element Algorithm for Thermal Darcy Flows with Variable Viscosity. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12747. Springer, Cham. https://doi.org/10.1007/978-3-030-77980-1_17

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  • DOI: https://doi.org/10.1007/978-3-030-77980-1_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77979-5

  • Online ISBN: 978-3-030-77980-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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