ABSTRACT

This chapter illustrates the explicit solution of the complete equations and introduces the simple link-node model network. For the four-point implicit method and most solution schemes discussed in the chapter, the unknowns are typically computed at cross-sections separated by some length. Boundary conditions may be flows or stage for the upstream boundary and flow, stage, or a rating curve at the downstream boundary. If the solution is purely kinematic, the convective momentum term in the momentum equation would be zero and the frictional and gravitational acceleration terms would be equal. Density variations caused by changes in water quality are usually insignificant in comparison with other terms in the momentum equation for streams and rivers. Although a relatively large number of implicit models are available, the most frequent usage has been in the prediction of water quantity variations rather than water quality variations.