Flow Through a System of Rivers

A river system consisting of a main-stem river and one or more tributaries is efficiently solved using an iterative relaxation method (Fread, 1973, 1985) in q = -c,ks{h - hcf2

which the flow at the confluence of the main-stem and tributary is treated as the lateral inflow/outflow (q) in Eqs. (29) and (30). This algorithm was extended so as to treat a dendritic system of waterways having nth-order tributaries (Lewis et al., 1996) and further extended to treat a river system that has any bifurcations such as islands, along with or without nth-order tributaries (Jin, et al., 2000). Also, a less versatile direct solution technique can be used (Fread, 1985), wherein three internal boundary equations conserve mass and momentum at each bifurcation or junction confluence. The resulting system of algebraic equations uses a special sparse matrix Gaussian elimination technique for an efficient solution (Fread, 1983).

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