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A modified Rusanov scheme for shallow water equations with topography and two phase flows

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Abstract.

In this work, we introduce a finite volume method for numerical simulation of shallow water equations with source terms in one and two space dimensions, and one-pressure model of two-phase flows in one space dimension. The proposed method is composed of two steps. The first, called predictor step, depends on a local parameter allowing to control the numerical diffusion. A strategy based on limiters theory enables to control this parameter. The second step recovers the conservation equation. The scheme can thus be turned to order 1 in the regions where the flow has a strong variation, and order 2 in the regions where the flow is regular. The numerical scheme is applied to several test cases in one and two space dimensions. This scheme demonstrates its well-balanced property, and that it is an efficient and accurate approach for solving shallow water equations with and without source terms, and water faucet problem.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Taibah University, P.O. Box 30002, 41477, Madinah, Saudi Arabia

    Kamel Mohamed

  2. Permanent Address: Department of Mathematics, Faculty of Science, Assiut University, New Valley, Egypt

    Kamel Mohamed

  3. LAGA, Université Paris 13, 99 Av.J.B.Clement, 93430, Villetaneuse, France

    F. Benkhaldoun

Authors
  1. Kamel Mohamed
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  2. F. Benkhaldoun
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Correspondence to Kamel Mohamed.

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Mohamed, K., Benkhaldoun, F. A modified Rusanov scheme for shallow water equations with topography and two phase flows. Eur. Phys. J. Plus 131, 207 (2016). https://doi.org/10.1140/epjp/i2016-16207-3

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  • DOI: https://doi.org/10.1140/epjp/i2016-16207-3

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