  A quasi-second order scheme is developed to obtain approximate solutions of
the shallow water equationswith bathymetry. The scheme is based on a staggered
finite volume scheme for the space discretization:the scalar unknowns are
located in the discretisation cells while the vector unknowns are located on
theedges (in 2D) or faces (in 3D) of the mesh. A MUSCL-like interpolation for
the discrete convectionoperators in the water height and momentum equations is
performed in order to improve the precisionof the scheme. The time
discretization is performed either by a first order segregated forward
Eulerscheme in time or by the second order Heun scheme. Both schemes are shown
to preserve the waterheight positivity under a CFL condition and an important
state equilibrium known as the lake at rest.Using some recent Lax-Wendroff type
results for staggered grids, these schemes are shown to be Lax-consistent with
the weak formulation of the continuous equations; besides, the forward Euler
schemeis shown to be consistent with a weak entropy inequality. Numerical
results confirm the efficiency andaccuracy of the schemes.

Numerical Analysis;Numerical Analysis