A broad-crested weir boundary condition in Finite Volume Shallow-water numerical models

In the literature, the weir boundary condition is usually implemented imposing the weir formula at the boundaries, but this is rigorous only in subcritical steady conditions, and a more general approach is required during transients. With acceptable approximation, the non-submerged broad-crested weir behaves as a bottom step where the energy is conserved and critical conditions are attained at the top. Taking advantage of this observation, the analytic solution of the Riemann problem for the Shallow-water Equations over a dry bottom step is considered in this paper, and the momentum and mass fluxes of the analytic solution of the Riemann problem are used to impose weakly the broad-crested non-submerged weir boundary condition in a Finite Volume scheme