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Accuracy of kinematic wave and diffusion wave approximations for time‐independent flows
Author(s) -
Singh V. P.,
Aravamuthan V.
Publication year - 1995
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.3360090704
Subject(s) - kinematic wave , froude number , kinematics , flow (mathematics) , boundary (topology) , diffusion , mathematical analysis , mathematics , mechanics , physics , range (aeronautics) , classical mechanics , thermodynamics , materials science , ecology , surface runoff , composite material , biology
Errors 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 0 2(⩾ 7.5), where K is the kinematic wave number and F 0 is the Froude number. Even for small values of KF 0 2(e.g. KF 2 0 = 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 0 2= 7.5 and was greater than 30% for smaller values of KF 0 2(⩽ 0.75). This error increased with strong downstream boundary control.