Open Channel Flow Equations -- Methods for Solving Algebraic Equations and Their Systems -- Numerical Solution of Ordinary Differential Equations -- Steady Gradually Varied Flow in Open Channels -- Partial Differential Equations of Hyperbolic and Parabolic Type -- Numerical Solution of the Advection Equation -- Numerical Solution of the Advection-Diffusion Equation -- Numerical Integration of the System of Saint Venant Equations -- Simplified Equations of the Unsteady Flow in Open Channel. This book offers a comprehensive approach to the numerical modeling of open channel flow, based on the author's own research in this field, as well as his experience as a lecturer. It provides the reader with: Coverage of the most important problems of open channel hydraulics, including steady and unsteady flow in a single channel and in a channel network, transport of dissolved substance, transport of energy and more; Unified derivation of the governing equations for all problems, based on the fundamental laws of mass, momentum and energy conservation; Comprehensive presentation of the numerical methods applied in open channel flow modeling, with particular regard to the solution of hyperbolic and parabolic partial differential equations, which govern many important flow and transport processes; Detailed description of the numerical algorithms applied to solve particular problems, with many examples of solutions; Accuracy analysis of the numerical algorithms using the modified equation approach; New insights into numerical solution of some classical problems of open channel hydraulics, e.g. steady varied flow in a channel of arbitrary geometry. In-depth analysis of the simplified flood routing models and their unphysical properties, including a proposition of an alternative Instantaneous Unit Hydrograph, valid for all simplified models. Written in accessible language, Numerical Modeling in Open Channel Hydraulics contains information useful for higher level undergraduate and postgraduate students of civil and environmental engineering faculties, as well as scientists and practitioners in the field of hydraulic engineering, especially those using existing numerical codes or developing their own ones.