Abstract
AbstractErrors in the kinematic wave and 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 KF (⩾ 7.5), where K is the kinematic wave number and F0 is the Froude number. Even for small values of KF (e.g. KF20 = 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 ⩽ x ⩽ 0.95 for KF = 7.5 and was greater than 30% for smaller values of KF (⩽ 0.75). This error increased with strong downstream boundary control.
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