Paper Info
Title
The Riemann problem for the shallow water equations with discontinuous topography: The wet-dry case.
Abstract
In this paper we consider Riemann problems for the shallow water equations with discontinuous topography whose initial conditions correspond to a wet–dry front: at time t=0 there is vacuum on the right or on the left of the step. Besides the theoretical interest of this analysis, the results may be useful to design numerical methods and/or to produce reference solutions to compare different schemes. We show that, depending on the state at the wet side, 0, 1, or 2 self-similar solutions can be constructed by composing simple waves. In problems with 0 solutions, the step acts as an obstacle for the fluid and physically meaningful solutions can be constructed by interpreting the problem as a partial Riemann problems for the homogeneous shallow water system. Some numerical results are shown where different numerical methods are compared. In particular, it is shown that, in the non-uniqueness cases, the numerical solutions can converge to one or to the other solution, what is the reason that explains the huge differences observed when different numerical methods are applied to the shallow water system with abrupt changes in the bottom.
Year
DOI
Venue
2019
10.1016/j.jcp.2018.11.019
Journal of Computational Physics
Keywords
Field
DocType
Shallow Water model,Well-balanced methods,Finite volume methods,Approximate Riemann solvers,High order methods
Waves and shallow water,Obstacle,Mathematical analysis,Homogeneous,Riemann hypothesis,Numerical analysis,Shallow water equations,Mathematics,Riemann problem
Journal
Volume
ISSN
Citations 
378
0021-9991
0
PageRank 
References 
Authors
0.34
8
2
Name
Order
Citations
PageRank
Carlos Parés135335.30
Ernesto Pimentel217721.23