online_muskingum_cunge_convergence_ratios:
Convergence ratios of the MuskingumCunge 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 MuskingumCunge 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 R_{1} and R_{2}, 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 S_{o}, rating exponent β, and flood wave timeofrise t_{r}), 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 R_{1}, and phase convergence ratio R_{2}. 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 timetorise: 1 ≤ t_{r} ≤ 720 [hr] Reach length: 1 ≤ Δx ≤ 10000 [m] Time interval: 0.1 ≤ Δt ≤ 24 [hr]
