Analytical treatment of source terms for complex channel geometry

Starting from the classical conservative form of the shallow water equations, the source term of the momentum balance equation was modified to increase computational stability. This was achieved by replacing the term representing the local bed slope by an alternative expression of the pressure effect due to cross-section irregularities in non-prismatic channels. The resulting mathematical model turns out to be particularly suitable for complex channel and natural river geometries, and also improves the computational stability for complicated flow conditions. The explicit finite difference MacCormack scheme was adopted for numerical implementation. The model was thoroughly tested using a set of numerical test cases involving various channel geometries and a wide range of flow conditions. The same simulations were compared also with the classical model and with other schemes. Finally, a real flood event on the Italian river Reno was simulated, to confirm the model suitability for natural channels.