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Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations

Author

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  • Sueet Millon Sahoo

    (Indian Institute of Technology Kharagpur)

  • T. Raja Sekhar

    (Indian Institute of Technology Kharagpur)

  • G. P. Raja Sekhar

    (Indian Institute of Technology Kharagpur)

Abstract

In this paper, we consider quasilinear hyperbolic system of balance laws describing one-dimensional nonhomogeneous shallow water equations with generalized Riemann initial data. We obtain exact solutions to the shallow water equations with friction by using differential constraint method. A special case of the obtained solution provides well known rarefaction wave to the homogeneous case of the governing equations. We construct a convenient example for the generalized Riemann problem and study the behavior of the solution profiles.

Suggested Citation

  • Sueet Millon Sahoo & T. Raja Sekhar & G. P. Raja Sekhar, 2020. "Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 1225-1237, September.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:3:d:10.1007_s13226-020-0460-2
    DOI: 10.1007/s13226-020-0460-2
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    References listed on IDEAS

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    1. K. Ambika & R. Radha, 2016. "Riemann problem in non-ideal gas dynamics," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(3), pages 501-521, September.
    2. Kuila, Sahadeb & Raja Sekhar, T. & Zeidan, D., 2015. "A Robust and accurate Riemann solver for a compressible two-phase flow model," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 681-695.
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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).

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