Mathematical and numerical modelling of rapid transients at partially lifted sluice gates

• Published in: Advances in water resources 2023-11, Vol.181, p.104562, Article 104562
• Main Authors: Cozzolino, Luca, Varra, Giada, Cimorelli, Luigi, Della Morte, Renata
• Format: Article
• Language: English
• Subjects: Dam-break; Exact solution; Finite volume method; Multiple solutions; Shallow water equations; Sluice gate
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2023.104562

•An improved analytic solution of the dam-break problem at partially lifted sluice gates is presented.•The dam-break analytic solution always exists for any set of initial conditions.•The problem exhibits multiple solutions and a novel disambiguation criterion is proposed.•The classic equilibrium approach for the gate treatment leads to unsatisfactory numerical results in the case of fast transients.•The results of a novel non-equilibrium approach compare well with exact solutions and laboratory dam-break experiments. In the present paper, we study the mathematical and numerical modelling of rapid transients at partially lifted sluice gates in the context of one-dimensional Shallow water Equations. First, improved exact solutions of the dam-break problem with partially lifted gate are presented, assuming (i) the dependence of the gate contraction coefficient on the upstream flow depth, and (ii) a viable definition of the submerged flow equation. We show that an exact dam-break solution always exists for any set of initial conditions, but there are also initial conditions for which the solution is multiple. To cope with this case, a novel disambiguation criterion based on the continuous dependence of the solution on the initial conditions is used to select the physically congruent choice amongst the alternatives. Finally, we present a one-dimensional Finite Volume numerical model for the approximate solution of the Shallow water Equations equipped with an approximate Riemann solver for the sluice gate treatment at cells interfaces. The numerical experiments show that the embedding of the steady state gate equations (equilibrium approach) into the approximate Riemann solver leads to unsatisfactory dam-break simulations, while a novel relaxed version of the gate equations (non-equilibrium approach) supplies results that are in agreement with both the novel exact solutions and the laboratory dam-break results available from the literature.