The report presents a detailed review of mathematical modeling of flows in alluvial streams. Various computer codes for this are presented and a model for simple-island case is prepared. Branched flows in open channels with alluvial conditions occur in natural and man-made systems. Analysis of such flows by mathematical modeling is important considering its applications in water resources and environmental engineering.
Models may be categorized based on (i) equations used (ii) numerical method applied and (iii) consideration of physical processes. The governing equations for water flow and sediment flow are presented. The equations to be satisfied at junctions are also presented. Solution strategies and their variations are also discussed.
Various numerical methods for the solution and governing equations are mentioned. Implementation of the boundary condition is also described. A large number of existing computer codes to study flows in alluvial streams is presented.
Performance of various models is problem dependent and no model is suitable for all types of problems. This is due to the poor understanding of the relation between flow and sediment transport.
Finally, a numerical scheme based on one-dimensional equations, a quasi-steady assumption and an uncoupled approach using explicit finite-difference method, is proposed. Although the model is expected to perform with greater efficiency and robustness, it is yet to be tested against measured data and needs further study.
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