Boundary conditions in finite volume schemes for the solution of shallow-water equations: the non-submerged broad-crested weir

The broad-crested weir can be regarded as a zone of rapid variation of the bottom elevation that is short with respect to the characteristic length of the considered domain, and for this reason it can be conceptually modelled as a bed step. In this paper, the solution of the Riemann problem for the shallow-water equations over a bed step is exploited in order to simulate the behaviour of the broad-crested weirs, when these are present at the boundaries of the numerical domain. 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 proposed approach is implemented into a finite volume model for the approximate solution of one-dimensional shallow-water equations. Several numerical tests are carried out in order to demonstrate its possibilities and promising capabilities.