Accuracy of the kinematic wave and diffusion wave approximations for time-independent flows with infiltration included

Abstract

Abstract:Errors in the kinematic wave and diusion wave approximation for time-independent (or steady-state) cases of channel¯ow with in®ltration were derived for three types of boundary conditions: zero¯ow at the upstream end, and critical¯ow depth and zero depth gradient at the downstream end. The diusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1 . 4% for KF 2 0 5 7 . 5, and up to 14% for KF 2 0 4 0 . 75 for the upstream boundary condition of zero discharge and ®nite depth, where K is the kinematic wave number and F 0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF 2 0 (41). The accuracy of these approximations was signi®cantly in¯uenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. #

A priori parameter estimates for a distributed, grid-based Xinanjiang model using geographically based information

“…Using the diffusion wave model for the hourly simulation, outflow of every grid cell is routed from cell to cell according to the upstream to downstream computation sequencing of grid cells (Li and Zhang, 2008). The diffusion wave model is employed for flow routing in GXM mainly for the following reasons: (1) it is appropriate for many cases of practical interest (Gonwa and Kavvas, 1986;Wang and Hjelmfelt, 1998;Singh and Aravamuthan, 1998), (2) its solution is usually independent of grid cell size (Jain et al, 2004), and (3) it can be reasonably used in hydraulically mild slopes (Jain and Singh, 2005). For daily simulation, flow routing module can be simplified because of the long concentration time (Zhao and Liu, 1995).…”

Study on effect of surface roughness on overland flow from different geometric surfaces through numerical simulation

“…() and Singh () have shown that in many cases, the dynamic wave and diffusion wave approximations give equally good representation of the St. Venant equation when used for overland flow routing. Singh and Aravamuthan (, ) investigated the accuracy of the diffusion wave approximation in comparison with the St. Venant equations for a variety of cases and found that diffusion wave approximation is sufficiently accurate for modeling over land flow as well as channel flow. Therefore, in the present study, a one‐dimensional solution of the diffusion wave approximation of the St. Venant equation is used to describe overland flow over different geometric surfaces.…”

Numerical simulations of large-scale cataclysmic floodwater: A simple depth-averaged model and an illustrative application

“…Although numerical solutions are possible, the typically employed algorithms use short time steps, which incur very large computational costs (Ferrick, 1985). Hence, various kinds of approximation methods have been developed (e.g., Parlange et al, 1990;Singh, 1994;Bajracharya and Barry, 1997;Singh and Aravamuthan, 1998). Before considering the further simplification of Eq.…”