Unified Streamflow Routing by Finite Elements

A deterministic finite element model is developed for streamflow routing. The simultaneous solution of the continuity and momentum equations results in a complete flow model that uses the Galerkin finite element technique and a dimensionless time‐weighting factor. The solution for the depth of flow, velocity of flow, and discharge obtained through the Newton‐Raphson iterative equation solver is found to be unconditionally stable for the time‐weighting factor between 0.55 and 1.0. The model shows great promise for the simulation of flow in natural channels as illustrated in a test problem of the Illinois River in Oklahoma. Simulated flows at 50.4 miles (80.6 km) downstream from the Watts station compared favorably with the observed flows at the Tahlequah station. Results of application of the model are in close agreement with those of an explicit finite difference model tested. Application to an idealized rectangular channel not only defines the stable range of the time‐weighting factor but also its influence in minimizing attenuation that results from the use of large time steps.