  The present paper deals with the modelling of rapid transients at partially
lifted sluice gates from both a mathematical and numerical perspective in the
context of the Shallow water Equations (SWE). First, an improved exact solution
of the dam-break problem is presented, assuming (i) the dependence of the gate
contraction coefficient on the upstream flow depth, and (ii) a physically
congruent definition for the submerged flow equation. It is shown that a
relevant solution always exists for any set of initial conditions, but there
are also initial conditions for which the solution is multiple. In the last
case, a novel disambiguation criterion based on the continuous dependence of
the solution on the initial conditions is used to select the physically
congruent one among the alternatives. Secondly, a one (1-d) and a
two-dimensional (2-d) form of a SWE Finite Volume numerical model, equipped
with an approximate Riemann solver for the sluice gate treatment at cells
interfaces, are presented. It is shown that the numerical implementation of
classic steady state gate equations (classic equilibrium approach) leads to
unsatisfactory numerical results in the case of fast transients, while a novel
relaxed version of these equations (non-equilibrium approach) supplies very
satisfactory results both in the 1-d and 2-d case. In particular, the 1-d
numerical model is tested against (i) the proposed novel exact solutions and
(ii) recent dam-break laboratory results. The 2-d model is verified by means of
a test in a realistic detention basin for flood regulation, demonstrating that
the novel findings can be promptly applied in real-world cases.
