Ali Triki and Ezzeddine Hadj-Taïeb
1D open channel transient flow, finite element method, shallow water, shock-capturing, transcritical flows, subcritical flow, flood wave
An efficient and accurate solution algorithm is developed for 1D unsteady flow problems in open channels. The method was the finite element solution of the Saint-Venant equations using the bi-tridiagonal matrix algorithm. For numerical stability, the time step was a function of depth and flow velocity, to avoid restriction due to the wave celerity variation in the computational analysis when using the method of characteristics. Validity of numerical models is obvious compared with the experimental data. Two examples were solved with the finite element method (FEM). The first involves routing a discharge hydrograph down a rectangular channel. The second example consists of routing a sudden shut off of all flow at the downstream end of the channel. These examples are taken from the text book of Streeter and Wylie [Hydraulic transients (Ann Arbor: F.E.B. Press, 1983)]. Numerical results agree well with those obtained by these authors and show that the proposed method is consistent, accurate and highly stable in capturing discontinuities propagation in free surface flows.
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