Numerical modeling of unsteady flow: implicit scheme revisited

The movement of flow in open channels and natural streams is basically governed by the continuity and momentum equations. These equations consist of a system of partial differential hyperbolic equations while various analytical and numerical methods have been recommended for solving this system. In this study, the formulation of a robust four -point implicit scheme is revisited with the step-by-step derivation details. By applying this scheme, the governing equations turns into a system of nonlinear algebraic equations, which can be solved iteratively using the generalized Newton-Raphson scheme. Although the value of resistance coefficient has an inevitable impact on the routing results, the effect of inappropriate estimation of the roughness coefficient has not been quantified in the hydraulic flow routing results. The conducted numerical experiment demonstrates that the routing results are significantly affected by the selected values for Manning’s coefficient

Keywords:

Open channel hydraulics , hydraulic flow routing , implicit finite difference scheme , resistance equation , Manning’s coefficient.