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The Riemann problem for the shallow water equations with horizontal temperature gradients

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  • Thanh, Mai Duc

Abstract

We consider the Riemann problem for the system of shallow water equations with horizontal temperature gradients (the Ripa system). The model under investigation has the form of a nonconservative system, and it is hyperbolic, but is not strictly hyperbolic. We construct all solutions of the Riemann problem. It turns out that there may be up to three distinct solutions. A resonant phenomenon which causes the colliding shock waves is observed, where multiple waves associated with different characteristic fields propagate with the same shock speed.

Suggested Citation

  • Thanh, Mai Duc, 2018. "The Riemann problem for the shallow water equations with horizontal temperature gradients," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 159-178.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:159-178
    DOI: 10.1016/j.amc.2017.12.031
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    References listed on IDEAS

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    1. Cuong, Dao Huy & Thanh, Mai Duc, 2015. "A Godunov-type scheme for the isentropic model of a fluid flow in a nozzle with variable cross-section," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 602-629.
    2. Cuong, Dao Huy & Thanh, Mai Duc, 2017. "Constructing a Godunov-type scheme for the model of a general fluid flow in a nozzle with variable cross-section," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 136-160.
    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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    Cited by:

    1. Jana, Sumita & Kuila, Sahadeb, 2022. "Exact solution of the flux perturbed Riemann problem for Cargo-LeRoux model in a van der Waals gas," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Thanh, Mai Duc & Cuong, Dao Huy, 2020. "Building a van Leer-type numerical scheme for a model of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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    2. Cuong, Dao Huy & Thanh, Mai Duc, 2017. "Constructing a Godunov-type scheme for the model of a general fluid flow in a nozzle with variable cross-section," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 136-160.
    3. Thanh, Mai Duc & Cuong, Dao Huy, 2020. "Building a van Leer-type numerical scheme for a model of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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