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Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations

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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.

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Acknowledgement

Authors would like to thank the reviewers for their valuable comments and suggestions to improve the quality of the manuscript. The first author would like to thank Professor Natale Manganaro and Professor carmela curro from Department of Mathematics, Universit Degli Studi Di Messina, Messina for their valuable suggestions. First author is highly thankful to Ministry of Human Resource Development, Government of India, for the institute fellowship (grant no. IIT/ACAD/PGS & R/F.II/2/14MA92R02).

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Sueet Millon Sahoo, T. Raja Sekhar & G. P. Raja Sekhar

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  1. Sueet Millon Sahoo
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  2. T. Raja Sekhar
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  3. G. P. Raja Sekhar
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Correspondence to T. Raja Sekhar or G. P. Raja Sekhar.

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Sahoo, S.M., Raja Sekhar, T. & Raja Sekhar, G.P. Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations. Indian J Pure Appl Math 51, 1225–1237 (2020). https://doi.org/10.1007/s13226-020-0460-2

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  • DOI: https://doi.org/10.1007/s13226-020-0460-2

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