Study of the adaptive refinement Process on an open source 2D shallow-water flow solver using quadtree grid for flood simulations.

The full resolution of shallow-water equations for modeling flash floods may have a high computational cost, so that majority of flood simulation softwares used for flood forecasting use a simplification of this model which permit to save a lot of computational time by sacrificing in an unquantified way the precision of simulations. To reduce drastically the cost of such 2D simulations by quantifying the lost of precision, we propose a 2D shallow-water flow solver built with the open source code Basilisk [1], which is using adaptive refinement on a quad-tree grid. We perform a systematic study of the impact of the chosen criterion for adaptive refinement  on the Tewkesbury flood of july 2007. The criterium which has the best computational time / precision ratio is proposed. Finally, we present the power law giving the computational time in respect to the maximum resolution and we show that this law for our 2D simulation is close to the one of 1D simulation, thanks to the fractal dimension of the topography.

We use this criterion to perform the simulation of the flood of Cannes (03-10-2015). We show that our simulation are faster than the event. We also show that our simulation predict accurately the areas hardly touched by the flood. 

[1] http://basilisk.fr/