Analysis and Approximation of Conservation Laws with Source Terms
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Scientific Computing
A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems
Journal of Scientific Computing
Hyperconcentrated 1D Shallow Flows on Fixed Bed with Geometrical Source Term Due to a Bottom Step
Journal of Scientific Computing
Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow
Journal of Computational Physics
A Riemann solver for unsteady computation of 2D shallow flows with variable density
Journal of Computational Physics
Energy balance numerical schemes for shallow water equations with discontinuous topography
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
In this paper we present the exact solution of the Riemann problem for the non-linear shallow water equations with a step-like bottom. The solution has been obtained by solving an enlarged system that includes an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step. The resulting solution is unique and satisfies the principle of dissipation of energy across the shock wave. We provide examples of possible wave patterns. Numerical solution of a first-order dissipative scheme as well as an implementation of our Riemann solver in the second-order upwind method are compared with the proposed exact Riemann problem solution. A practical implementation of the proposed exact Riemann solver in the framework of a second-order upwind TVD method is also illustrated.