Technical Report

Sponsor: GWRI

Start Date: 2000-03-01; Completion Date: 2001-02-28;

Keywords: Hydrodynamic Models, Open Channel Flow, Numeric Simulation

Summary:

In this report, we develop a two-dimensional hydrodynamic model for simulating swallow-water open-channel flows using depth-averaged equations. The model is capable of handling arbitrarily shaped channel geometries such as those typically encountered in natural rivers. The time-dependent, depth-averaged equations are formulated in generalized, non-orthogonal curvilinear coordinates so that complex river reaches can be accurately modeled using body-fitted computational grids. The equations are discretized in space using a conservative second-order accurate finite-volume method. Adaptive artificial dissipation terms, with scalar and matrix-valued scaling, are explicitly introduced into the discrete equations to ensure that the resulting scheme is applicable to all flow regimes and can accurately capture hydraulic jumps. The discrete equations are integrated in time using a four-stage Runge-Kutta method. For steady-state computations the convergence of the Runge-Kutta algorithm is enhanced using local time stepping, implicit residual smoothing, and multigrid acceleration. Time accurate solutions may also be obtained by integrating the governing equations in time using the four-stage, second-order accurate in time, Runge-Kutta scheme without implementing the aforementioned convergence acceleration measures.

To validate the numerical model, we carry out calculations for a variety of open channel flows for which experimental data have been reported in the literature. The calculated test cases include flow in strongly curved channels and channel expansions. For all cases considered the numerical method is shown to yield solutions of comparable accuracy to those reported in earlier studies in the literature using depth-averaged equations. Discrepancies between predictions and experiments are observed only for very strongly curved channels for which three-dimensional effects dominate.

Due to the lack of detailed bathymetry and flow measurement data for the ACT and ACF basins, the present numerical model was not applied to a real-life reach as was initially intended. This not withstanding, however, the method has been designed to be sufficiently general and its application to a natural geometry is straightforward. The good overall agreement between measurements and numerical simulations for the test cases considered in this report suggests that the present method could serve as a powerful computational tool for understanding the complex flow patterns in the ACT and ACF basins and for guiding the development of simpler one-dimensional models.