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Technique for implicit dynamic routing in rivers with tributaries
Author(s) -
Fread D. L.
Publication year - 1973
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr009i004p00918
Subject(s) - tributary , extrapolation , interval (graph theory) , flow (mathematics) , nonlinear system , transient (computer programming) , streamflow , shallow water equations , limit (mathematics) , stage (stratigraphy) , stability (learning theory) , mathematics , differential equation , flow routing , computer science , geology , geotechnical engineering , mathematical analysis , geometry , physics , geography , cartography , drainage basin , paleontology , combinatorics , quantum mechanics , machine learning , operating system
The prediction of transient flow in a river having a major tributary poses a challenging problem for the streamflow forecaster. The interaction of storage and dynamic effects between the two rivers can be simulated efficiently by a mathematical model consisting of the two unsteady flow differential equations and of known stage time, discharge time, or stage discharge relationships at the extremities of the rivers. Numerical solutions of discharge and water surface elevation are obtained from the differential equations at specified time intervals by an implicit finite difference technique. This produces successive systems of nonlinear equations that are efficiently solved by the Newton‐Raphson iterative method in combination with an extrapolation procedure and a specialized direct method for solving a system of linear equations. The length of the specified time interval is not limited by computational stability; however, accuracy constraints may limit its size. Some numerical results are presented to illustrate the interaction between a river and a tributary when they are subjected to a flood wave of long duration.