# Shallow Water Model

## Mathematical model

SW2D solves the 2D shallow water equations: $Latex formula$ $Latex formula$

where $Latex formula$ (resp. $Latex formula$ and $Latex formula$) is the time (resp. space), $Latex formula$ the gravitational acceleration, $Latex formula$ represents the water depth, $Latex formula$ (resp. $Latex formula$) the unit-discharge in the $Latex formula$ (resp. $Latex formula$) direction, $Latex formula$ (resp. $Latex formula$) the bottom slope in the $Latex formula$ (resp. $Latex formula$) direction and $Latex formula$ (resp. $Latex formula$) the friction slope in the $Latex formula$ (resp. $Latex formula$) direction estimated using the classical Strickler formulation: $Latex formula$ $Latex formula$

## Numerical scheme

The shallow water equations are discretized using a finite volume approach: $Latex formula$

The fluxes and the source terms are estimated using an explicit method. The fluxes through the interfaces $Latex formula$ are estimated using the HLL/HLLC Riemann solver.