online_muskingum_cunge_convergence_ratios:
Convergence ratios of the Muskingum-Cunge method
This set of two online calculators: (1)
Online_Muskingum_Cunge_convergence_ratios, and (2) Online_Muskingum_Cunge_convergence_ratios_practical, are intended to help the user of
the Muskingum-Cunge method of flood routing choose the
numerical parameters (grid resolution) that will provide sufficient accuracy for a given problem.
The calculator Online_Muskingum_Cunge_convergence_ratios is recommended for use when a
first approximation on convergence is indicated. This calculator inputs spatial resolution L/Δx, Courant number C,
and weighting factor X. The calculator outputs amplitude and phase convergence ratios R1 and
R2, respectively. The latter values should be as close to 1, but less than 1, as possible,
e.g., 0.9995.
The calculator Online_Muskingum_Cunge_convergence_ratios_practical is recommended for use when a
second approximation on convergence is indicated.
This calculator inputs hydraulic variables (mean velocity u, mean flow depth d,
mean channel slope So,
rating exponent β, and flood wave time-of-rise tr), and numerical parameters
(reach length Δx
and time interval Δt). The calculator
outputs
spatial resolution L/Δx, Courant number C,
cell Reynolds number D, weighting factor X, amplitude convergence ratio
R1, and phase convergence ratio
R2. The convergence ratios should be as close to 1, but less than 1, as possible,
e.g., 0.9995.
Allowable range of values for Online_Muskingum_Cunge_convergence_ratios:
Weighting factor: 0 ≤ X ≤ 1
Spatial resolution: 10 ≤ L /Δx ≤ 400
Courant number: 0.1 ≤ C ≤ 10
Allowable range of values for Online_Muskingum_Cunge_convergence_ratios_practical:
Mean velocity: 0.1 ≤ u ≤ 10 [m/s]
Mean flow depth: 0.1 ≤ d ≤ 100 [m]
Mean channel slope: 0.00001 ≤ u ≤ 0.1 [m/m]
Rating exponent: 1 ≤ β ≤ 5/3 • [May leave blank to specify default β = 5/3]
Flood wave time-to-rise: 1 ≤ tr ≤ 720 [hr]
Reach length: 1 ≤ Δx ≤ 10000 [m]
Time interval: 0.1 ≤ Δt ≤ 24 [hr]