Analysis of interpolation strategies in a fixed-grid method of characteristics in transient open channel flow.

摘要

The computer modeling of unsteady open channel flow is a challenging problem in the computational hydraulics discipline and many methods of solution have been proposed. The fixed-grid method of characteristics (MOC) has been widely used in the numerical computation of transient flow in open channels. However, in this method wave paths do not directly coincide with computational grid points, hence the use of interpolation techniques is inevitable. The significance of the thesis is primarily in its insight and understanding of information propagation in transient open channel flow. Specifically this thesis focuses on various interpolation techniques associated with MOC for the solution of transient open channel flow. A multi-mode interpolation scheme is developed that enables the user to easily choose from different interpolation methods. The linear methods consist of space-line, time-line and flexible discretization methods while the non-linear methods include cubic spline and truncated spline interpolation.; It is shown that flexible discretization methods are easily implemented and have reasonable accuracy. The effects of various interpolation methods on three different case studies are investigated in detail. The cubic spline approach is fastest to converge, followed by time-line and space-line interpolation methods. Moreover, the cubic spline interpolation exhibits the lowest mass balance error, followed by time-line and space-line interpolations using different grid sizes. The truncated spline avoids the tendency of cubic spline to over- or under-predict interpolated points.; The effect of cubic spline and space-line interpolations on depth profile has been studied in channels with lateral inflow under both subcritical and supercritical flow. The numerical results are compared with experimental data and the cubic spline results are in close agreement, having an average error half of that from the space-line method. Overall, the cubic spline method is the more promising and robust interpolation technique.; This thesis has also taken the first step in developing an advection-reaction model for channels with fully-transient hydraulic conditions using MOC. The model is partially verified through comparisons to analytical solutions under steady condition. The effect of various interpolation methods on concentrations is investigated.