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Resolution of the bidimensional shallow water equations with horizontal temperature gradients by a well Balanced Roe scheme

Author

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  • Jelti, S.
  • Serghini, A.
  • Elmahi, I.

Abstract

This work presents a numerical resolution of the two-dimensional Ripa system using Roe scheme. A discretization of the source term satisfying the conservation property is presented. The mathematical model is based on the ordinary shallow water equations in merging the horizontal temperature gradient. The numerical approach employs unstructured grids and integrates Runge–Kutta method and the minmod limiter to achieve second order accuracy in both time and space domains. A strategy of mesh adaptation based on temperature gradient is implemented to refine the study domain and gain in computational cost. Various numerical tests are conducted to verify the efficiency of the numerical method.

Suggested Citation

  • Jelti, S. & Serghini, A. & Elmahi, I., 2025. "Resolution of the bidimensional shallow water equations with horizontal temperature gradients by a well Balanced Roe scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 423-437.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:423-437
    DOI: 10.1016/j.matcom.2024.10.025
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    References listed on IDEAS

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    1. Jelti, S. & Boulerhcha, M., 2022. "Numerical modeling of two dimensional non-capacity model for sediment transport by an unstructured finite volume method with a new discretization of the source term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 253-276.
    2. Gordon Chih-Ming Ku & I-Wei Shang, 2020. "Using the Integrated Kano–RIPA Model to Explore Teaching Quality of Physical Education Programs in Taiwan," IJERPH, MDPI, vol. 17(11), pages 1-13, June.
    3. Sánchez-Linares, C. & Morales de Luna, T. & Castro Díaz, M.J., 2016. "A HLLC scheme for Ripa model," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 369-384.
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