Author(s): Taban Sowlati; Bryan W. Karney
Linked Author(s): Bryan W. Karney
Keywords: Unsteady open channel flow; Interpolation techniques; Method ofcharacteristics
Abstract: The method of characteristics (MOC) has been widely used in the numerical computation of transient flow in closed conduits and open channels. This method, particularly in open channels and complex systems, has one significant drawback: exactly satisfying the Courant condition is impossible in almost all practical systems. Therefore, interpolation methods must be used and these inevitably produce physical and numerical errors. Numerical techniques associated with the use of the fixed-grid MOC are studied here in order to minimize the interpolation errors in transient open channel flow. Various methods are compared via two case studies: (a) a trapezoidal channel with an upstream reservoir and a downstream control valve and (b) a rectangular channel with a specified inflow hydrograph. Error is assessed through the mass balance, the simulated behavior and the time of occurrence of extreme depths for different grid sizes. The truncated spline can be used to avoid the tendency of conventional splines to over-or under-predict interpolated points; conventional cubic splines tend to have the lowest volumetric error for different grid sizes; and time-line methods tend to have consistent minimum depths at different levels of discretization. Results based on case (b) show that depth profiles obtained by cubic splines, and indeed for time-line interpolations, are consistent for different time steps and thus both techniques have the desirable property of grid insensitivity, unlike the space-line interpolation technique. Depending on the application, both cubic spline and time-line interpolations tend to perform well even with a relatively large time step, whereas space-line interpolation requires a smaller time step to obtain a similar accuracy.
Year: 2001