This work is licensed under the Creative Commons Attribution-NonCommercial- NoDerivatives 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. The final version of this paper is published by Elsevier, and available at the link: https://doi.org/10.1016/j.advwatres.2019.103422 Flood propagation modelling with the Local Inertia Approximation: theoretical and numerical analysis of its physical limitations Luca Cozzolino 1 , Luigi Cimorelli 2 , Renata Della Morte 3 , Giovanni Pugliano 4 , Vincenzo Piscopo 5 , Domenico Pianese 6 Abstract 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, whose physical basis is discussed here, 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 a shock is always developed at moving wetting-drying frontiers, and this justifies the study of the 1 Sen. Res., Ph. D., Dept. of Engrg., Parthenope Univ., Centro Direzionale di Napoli – Is. C4, 80143 Napoli, Italy. E- mail: luca.cozzolino@uniparthenope.it 2 Sen. Res., Ph. D., Dept. of Civil, Architectural and Environmental Engrg., Federico II Univ., via Claudio 21, 80125 Napoli, Italy. E-mail: luigi.cimorelli@unina.it 3 Full Prof., Ph. D., Dept. of Engrg., Parthenope Univ., Centro Direzionale di Napoli – Is. C4, 80143 Napoli, Italy. E- mail: renata.dellamorte@uniparthenope.it 4 Ass. Prof., Ph. D., Dept. of Engrg., Parthenope Univ., Centro Direzionale di Napoli – Is. C4, 80143 Napoli, Italy. E- mail: giovanni.pugliano@uniparthenope.it 5 Jun. Res., Ph. D., Dept. of Sci. and Tech., Parthenope Univ., Centro Direzionale di Napoli – Is. C4, 80143 Napoli, Italy. E-mail: vincenzo.piscopo@uniparthenope.it 6 Full Prof., Dept. of Civil, Architectural and Environmental Engrg., Federico II Univ., via Claudio 21, 80125 Napoli, Italy. E-mail: pianese@unina.it