Flood propagation modeling with the Local Inertia Approximation: Theoretical and numerical analysis of its physical limitations

摘要: Abstract Attention of the researchers has increased towards a simplification complete Shallow water Equations called Local Inertia Approximation (LInA), which is obtained by neglecting advection term in momentum conservation equation. This model, whose physical basis discussed here, commonly used for simulation slow flooding phenomena characterized small velocities and absence flow discontinuities. In present paper it demonstrated that shock always developed at moving wetting-drying frontiers, this justifies study Riemann problem on even uneven beds. particular, general exact solution horizontal frictionless bed given, together with non-breaking wave propagating friction, while some example given discontinuous bed. From analysis, follows drying wet forbidden LInA there are initial conditions no smoothly varying addition, propagation flood sloping impossible if drops height same order magnitude moving-frontier height. Finally, found mechanical energy violated. It evident all these findings pose severe limit to application model. The numerical analysis confirmed existence frontal advancing flows, but also models may produce solutions, unreliable because mere algorithmic nature, case mathematical solutions do not exist. Following preceding results, two criteria definition applicability limits model have been considered. These criteria, valid very restrictive continuously elevation, based limitation wetting front velocity spurious total head variations, respectively. Based discouragingly severe, elevation varies continuously. More important, non-existence topography receding fronts radically question viability realistic cases. classic SWE should be preferred majority practical applications.