  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.
