The analytic solution of the Shallow-Water Equations with partially open sluice-gates: The dam-break problem

• The dam-break problem with partial opening of the sluice-gate is solved.
• The problem exhibits multiple solutions and a disambiguation criterion is required.
• The numerical schemes must be able to cope with multiple solutions.
• There are cases where no analytic solution is possible.
• Simple numerical schemes cannot detect the cases with no analytic solution.

The general solution of the dam-break problem with partial uplift of the sluice-gate is presented in the framework of the one-dimensional Shallow-Water Equations, under the hypothesis that the classic Energy–Momentum (E–M) formulation is used to evaluate the flow characteristics at the gate. Due to the nonlinearity of the problem, there are ranges of the initial conditions for which the problem admits multiple solutions, or no solution. In the ranges in which there are multiple solutions, the maximization of the discharge under the gate is used as a disambiguation criterion. The exact solutions are used as a benchmark in order to evaluate the results of a simple Finite-Volume scheme, where the discharge under the gate and the forces exerted on the flow by the gate itself are calculated using the E–M formulation.