Flood propagation modelling with the Local Inertia Approximation: theoretical and numerical analysis.

Attention of the researchers has increased towards a simplification of the complete Shallow water Equations called the Local Inertia Approximation (LInA), which is obtained by neglecting the advection term in the momentum conservation equation. This model is commonly used for the simulation of slow flooding phenomena characterized by small velocities and absence of flow discontinuities. In the present paper it is demonstrated that discontinuities are always developed at moving wetting-drying frontiers, and this justifies the study of the Riemann problem on even and uneven beds. In particular, the general exact solution for the Riemann problem on horizontal frictionless bed is given, together with the exact solution of the non-breaking wave propagating on horizontal bed with friction, while some example solution is given for the Riemann problem on discontinuous bed. From this analysis, it follows that drying of the wet bed is forbidden in the LInA model, and that there are initial conditions for which the LInA has no solution. In addition, the numerical analysis has confirmed that non-conservative schemes cannot be used for the propagation of the LInA on dry bed, because they converge to a wrong solution. Following the preceding results, two new criteria for the definition of the applicability limits of the LInA model have been proposed, based respectively on the limitation of the wetting front velocity and the limitation of spurious total head variations