ACCURACY OF KINEMATIC WAVE AND DIFFUSION WAVE APPROXIMATIONS FOR TIME-INDEPENDENT FLOWS

Errors in the kinematic wave acid diffusion wave approximations for time-independent (or steady-state) cases of channel flow were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors in the range 1-2% for values of KF02 (greater than or equal to 7.5), where K is the kinematic wave number and F-0 is the Froude number. Even for small values of KF02 (e.g. KF02 = 0.75), the errors were typically less than 15%. The accuracy of the diffusion wave approximation was greatly influenced by the downstream boundary condition. The error of the kinematic wave approximation was found to be less than 13% in the region 0.1 less than or equal to x less than or equal to 0.95 for KF02 = 7.5 and was greater than 30% for smaller values of KF02 (less than or equal to 0.75). This error increased with strong downstream boundary control.