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ABSTRACT
In open channel networks, flow is usually approximated by the one-dimensional (1D) Saint-Venant equations coupled with an empirical junction model. In this work, a comparison in terms of accuracy and computational cost between a coupled 1D-2D shallow water model and a fully two-dimensional (2D) model is presented. The paper explores the ability of a coupled model to simulate the flow processes during supercritical flows in crossroads. This combination leads to a significant reduction in the computational time, as a 1D approach is used in branches and a 2D approach is employed in selected areas only where detailed flow information is essential. Overall, the numerical results suggest that the coupled model is able to accurately simulate the main flow processes. In particular, hydraulic jumps, recirculation zones, and discharge distribution are reasonably well reproduced and clearly identified. Overall, the proposed model leads to a 30% reduction in run times.
Notation
| A | = | = area (m2) |
| B | = | = channel width (m) |
| E, F, G | = | = flux vectors (–) |
| g | = | = gravity acceleration (ms−2) |
| h | = | = water depth (m) |
| J | = | = Jacobian matrix (–) |
| l | = | = length of an edge (m) |
| n | = | = normal vector (–) |
| nM | = | = Manning's roughness coefficient (sm–1/3) |
| Q | = | = flow discharge (m3 s–1) |
| S | = | = source term (–) |
| S0 | = | = bed slope (m2 s–2) |
| Sf | = | = friction slope (m2 s–2) |
| t | = | = time (s) |
| U | = | = conservative variables (–) |
| u, v | = | = velocities in the x and y directions (m s–1) |
| x, y | = | = Cartesian coordinates (m) |
| Δt | = | = time step (s) |
Subscripts
| d | = | = downstream branch |
| u | = | = upstream branch |