Robust finite volume schemes and variational inversions for 2D shallow water models. Application to flood plain dynamics

This study proposes original combinations of higher order Godunov type finite volume schemes and time discretization schemes for the 2d shallow water equations, leading to fully second-order accuracy with well-balanced property. Also accuracy, positiveness and stability properties in presence of dynamic wet/dry fronts is demonstrated. The test cases are the classical ones plus extra new ones representing the geophysical flow features and difficulties. Preliminary numerical experiments give some key features between the topography representation scale and the grid size, and depending on the scheme order. A second aspect aims at performing sensitivities analysis and variational data assimilation, based on the adjoint model. Original sensitivity maps with respect to the basal (roughness, topography) fields are discussed. Inflow discharges and roughness coefficients spatially distributed are efficiently inferred on a real-like flood plain test case.