Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations

Sueet Millon Sahoo, T. Raja Sekhar () and G. P. Raja Sekhar ()
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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

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 1225-1237

Abstract: 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.

Keywords: Generalized Riemann problem; exact solutions; differential constraint method; non-homogeneous shallow water equations; 35L60; 35L45; 35Q53; 74G05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-020-0460-2

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