Finite element modeling of surge propagation and an application to the Hay River, N.W.T.

This paper describes the application of the characteristic-dissipative-Galerkin method to steady and unsteady open channel flow problems. The robust performance of this new finite element scheme is demonstrated in modeling the propagation of ice jam release surges over a 500 km reach of the Hay River in Alberta and Northwest Territories. This demonstration includes the automatic determination of steady flow profiles through supercritical–subcritical transitions, establishing the initial conditions for the unsteady flow analyses. The ice jam releases create a dambreak type of problem which begins as a very dynamic situation then develops into an essentially kinematic wave problem as the disturbance propagated downstream. The characteristic-dissipative-Galerkin scheme provided stable solutions not only for the extremes of dynamic and kinematic wave conditions, but also through the transition between the two. Key words: open channel flow, finite element method, dam break, surge propagation.

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Determination of longitudinal dispersion coefficients in open channel flow

10.3133/25218 ◽

1966 ◽

Keyword(s):

Channel Flow ◽

Open Channel ◽

Open Channel Flow ◽

Longitudinal Dispersion ◽

Dispersion Coefficients

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Interaction of buoyant plumes in open-channel flow

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000007165 ◽

1992 ◽

Vol 33 (4) ◽

pp. 451-473

Author(s):

P. J. Wicks

Keyword(s):

Diffusion Equation ◽

Channel Flow ◽

Open Channel ◽

Nonlinear Term ◽

Initial Conditions ◽

Hermite Polynomials ◽

Open Channel Flow ◽

The Other ◽

Buoyant Plumes ◽

Rich Variety

AbstractIn this paper, a model for lateral dispersion in open-channel flow is studied involving a diffusion equation which has a nonlinear term describing the effect of buoyancy. The model is used to investigate the interaction of two buoyant pollutant plumes. An approximate analytic technique involving Hermite polynomials is applied to the resulting PDEs to reduce them to a system of ODEs for the centroids and widths of the two plumes. The ODEs are then solved numerically. A rich variety of behaviour occurs depending on the relative positions, widths and strengths of the initial discharges. It is found that for two plumes of equal strength and width discharged side-by-side, the plumes move apart and the rate of spreading is inhibited by their interaction, whereas when one plume is initially much wider than the other, both plumes tend to drift to the side of the narrower plume. Finally, the PDEs are solved numerically for two sets of initial conditions and a comparison is made with the ODE solutions. Agreement is found to be good.

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The use of a one-dimensional depth-averaged moment of momentum equation for the nonhydrostatic pressure condition

Canadian Journal of Civil Engineering ◽

10.1139/l96-015 ◽

1996 ◽

Vol 23 (1) ◽

pp. 150-156 ◽

Cited By ~ 6

Author(s):

Yee-Chung Jin ◽

Baozhu Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Channel Flow ◽

Open Channel ◽

Open Channel Flow ◽

Momentum Equation ◽

Nonuniform Flow ◽

Pressure Condition ◽

Nonhydrostatic Pressure ◽

Averaged Model

A depth-averaged model formulated in the Cartesian coordinate system for curved open-channel flows is extended to solve problems where the effects of nonhydrostatic pressure distribution and nonuniform velocity distribution are significant. The nonhydrostatic pressure condition is added to the z-direction momentum equation assuming that the pressure deviation from the hydrostatic condition at the channel bed decreases linearly to the water surface. The pressure-effect terms are modified in both the moment of momentum and momentum equations. The resulting system of nonlinear equations is solved by a finite-element method. The derived model is then applied to four sophisticated nonuniform flow experiments from the literature. A comparison of the actual experimental results with their numerical prediction results, as calculated with the model, is presented. Generally speaking, a fairly good agreement for the depth-averaged velocities as well as reasonable perturbation profiles were obtained from this comparison. Therefore, it can be said that the depth-averaged model for open-channel flow is reasonably accurate under the given conditions. Key words: open-channel flow, depth-averaged method, finite-element method, nonhydrostatic pressure, nonuniform flow.

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