A Roe finite-volume scheme for 1D shallow water flows : wetting and drying simulation
Résumé
A finite-volume method for the one-dimensional shallow-water equations including topographic source terms is presented. Exploiting an original idea by Leroux, the system of partial-differential equations is completed by a trivial equation for the bathymetry. By applying a change of variable, the system is given a celerity-speed formulation, and linearized. As a result, an approximate Riemann solver preserving the positivity of the celerity can be constructed, permitting wetting and drying flow simulations to be performed. Finally, the simulation of numerical test cases is presented.
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