Communications in Mathematical Sciences

Volume 5 (2007)

Number 4

The Riemann problem for the shallow water equations with discontinuous topography

Pages: 865 – 885

DOI: http://dx.doi.org/10.4310/CMS.2007.v5.n4.a7

Authors

Philippe G. LeFloch

Mai Duc Thanh

Abstract

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.

Keywords

shallow water; conservation law; Riemann problem; discontinuous topography

2010 Mathematics Subject Classification

35L65, 76L05, 76N10

Full Text (PDF format)