Discontinuous Galerkin Finite-Element Method for Simulation of Flood in Crossroads

A numerical solution of the two-dimensional Saint Venant equations is presented for the study of the propagation of the floods through the crossroads of the city. The numerical scheme is a Runge-Kutta discontinuous Galerkin method (RKDG) with a slope limiter. The work studies the robustness and the stability of the method. The study is organized around three aspects: the prediction of the water depths, the location of the right and oblique hydraulic jumps in the crossing, and especially the distribution of the flow discharges in the downstream branches. The objective of this paper was to use the RKDG method in order to simulate supercritical flow in crossroads and to compare these simulations with experimental results and to show the advantage of this RKDG method compared to a second-order finite-volume method. A good agreement between the proposed method and the experimental data was found. The method is then able to simulate the flow patterns observed experimentally and to predict accurately the water depths, the location of the hydraulic jumps, and the discharge distribution in the downstream branches.