Boundary conditions in Finite Volume schemes for the solution of the Shallow-water Equations: the non-submerged broad-crested weir

The broad-crested weir can be regarded as a zone of smooth rapid variation of the bottom elevation that is short with respect to the characteristic length of the problem under exam, and then can be conceptually modelled as a bed step. In this paper, the solution of the Riemann problem for the Shallow-water Equation over a dry bed step is exploited in order to simulate the behaviour of the broad-crested weir during transients when these are present at the boundaries of the numerical domain in Finite Volume schemes. The issue of the multiplicity of solutions for this special Riemann problem is discussed, and rules are given in order to pick up the congruent solution among the alternatives. Finally, the approach proposed is implemented into a Spectral Volume model for the approximate solution of one-dimensional Shallow-water Equations, and it is demonstrated by means of numerical tests, showing its feasibility and its promising capabilities