Depth-Averaged Boussinesq Equations Applied to Flow in a Converging Channel

by Thomas Molls,
Gang Zhao,

Abstract: Supereritical flow in a contracting channel is simulated by numerically solving the 2D depth-averaged Boussinesq equations using a fmite-difference model DASH (Molls and Chaudhry 1995, Molls et al. 1995). To accomplish the time differencing, the model uses a second-order accurate Beam and Warming approximation; while, the spatial derivatives are approximated by second-order accurate central differencing. The equations are solved using an alternating direction-implicit (ADI) scheme. Due to the formation of cross waves, the water depth varies considerably in, and downstream of, the contraction and a non-hydrostatic pressure distribution is anticipated. To ascertain the importance of the Boussinesq terms, results are obtained with and without these terms. The numerical results are compared with experimental data reported by Ippen and Dawson (1951) for flow in a straight-walled contraction. The results indicate that including the Boussinesq terms does not significantly alter the converged solution.

Subject Headings: Boussinesq equations | Numerical models | Two-dimensional models | Model accuracy | Two-dimensional flow | Flow simulation | Channel flow | Water waves

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