  In this paper we propose a numerical method to solve the Cauchy problem based
on the viscous shallow water equations in an horizontally moving domain. More
precisely, we are interested in a flooding and drying model, used to modelize
the overflow of a river or the intrusion of a tsunami on ground. We use a non
conservative form of the two-dimensional shallow water equations, in eight
velocity formulation and we build a numerical approximation, based on the
Arbitrary Lagrangian Eulerian formulation, in order to compute the solution in
the moving domain.
