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Comprehensive text on the fundamentals of modeling flow and sediment transport in rivers treating both physical principles and numerical methods for various degrees of complexity. Includes 1-D, 2-D (both depth- and width-averaged) and 3-D models, as well as the integration and coupling of these models. Contains a broad selection of numerical methods for open-channel flows, such as the SIMPLE(C) algorithms on staggered and non-staggered grids, the projection method, and the stream function and vorticity method. The state-of-the-art in sediment transport modeling approaches is described, such as non-equilibrium transport models, non-uniform total-load transport models, and semi-coupled and coupled procedures for flow and sediment calculations. Sediment transport theory is discussed and many newly-developed, non-uniform sediment transport formulae are presented. The many worked examples illustrate various conditions, such as reservoir sedimentation; channel erosion due to dam construction; channel widening and meandering; local scour around in-stream hydraulic structures; vegetation effects on channel morphodynamic processes; cohesive sediment transport; dam-break fluvial processes and contaminant transport. Recommended as a reference guide for river and hydraulic engineers and as a course text for teaching sediment transport modeling, computational free-surface flow, and computational river dynamics to senior students.