The Riemann problem for the shallow water equations with discontinuous topography

Details The Riemann problem for the shallow water equations with discontinuous topography The Riemann problem for the shallow water equations with discontinuous topography

2007-12-21

arxiv.org/abs/0712.3778v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the existence of two-parameter wave sets, rather than wave curves. The selection of admissible waves is particularly challenging. Our construction is fully explicit, and leads to formulas that can be implemented numerically for the approximation of the general initial-value problem.

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