The multi-layer shallow water approach can be regarded as
a development of De Saint Venant equations in the
direction of a more accurate description of the physical
problem, keeping as far as possible the efficiency of
classical De Saint Venant numerical models. From this
point of view, in the present paper, the one dimensional
multi-layer De Saint Venant equations are briefly
developed, marking the fact that the stresses due to the
presence of neighboring layers can be treated as the effect
of a virtual topography. In this way, continuity and
momentum equation on each layer furnish a system of
equations that is very similar to classic single-layer De
Saint Venant equations.
This similitude suggests the possibility to solve the
resulting differential equations by means of the techniques
originally developed for the solution of De Saint Venant
equations. Following this idea, the 1D multi-layer De Saint
Venant equations are solved numerically by means of a
shock-capturing finite volume technique applied to each
layer separately.
The resulting numerical scheme is applied to some
benchmark test, and the results are presented and discussed.
