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A modified Rusanov method for simulating two-layer shallow water flows with irregular topography

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Abstract

In the current paper, we develop and suggest a modified Rusanov method for simulating two-layer shallow water flows with variable topography. The coupling between two-layers results in a non-conservative product term which involves the partial derivatives of unidentified physical parameters, as a result, the model is conditional hyperbolic. The stages of this scheme are predictor and corrector. A parameter for managing the numerical diffusion is included in the predictor stage, which is accomplished through the use of limiters theory. The balance conservation equation is recovered by the corrector stage. To prove the efficacy of the suggested scheme, we offer a number of numerical tests. The numerical outcomes indicate how accurate and well-balanced the suggested method is for simulating two-layer shallow flows with irregular topography.

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Acknowledgements

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number 445-9-583.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, New Valley University, Kharga, New Valley Governorate, Egypt

    Kamel Mohamed

  2. Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Kamel Mohamed

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  1. Kamel Mohamed
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Correspondence to Kamel Mohamed.

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Communicated by Abdellah Hadjadj.

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Mohamed, K. A modified Rusanov method for simulating two-layer shallow water flows with irregular topography. Comp. Appl. Math. 43, 136 (2024). https://doi.org/10.1007/s40314-024-02640-7

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  • DOI: https://doi.org/10.1007/s40314-024-02640-7

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