  We present a central differencing scheme for the solution of the shallow
water equations with non-flat bottom topography and moving wet-dry fronts. The
problem is numerically challenging due to two reasons. First, the non-flat
bottom topography requires accurate balancing of the source term of the
momentum conservation equation accounting for the gravitational force and the
flux gradient term accounting for the force due to pressure imbalance. Second,
the modelling of moving wet-dry fronts involves handling of diminishing water
height, which is numerically challenging to handle. The Riemann-solver free
scheme is fast, simple and robust. It successfully avoids negative water depths
at moving wet-dry boundaries and it exhibits good balancing between flux
gradients and source terms. The performance of the scheme is verified with a
number of test cases and the results compare favorably with published
analytical solutions.
