Numerical Modeling in Open Channel Hydraulics, 2010 Coll. Water Science and Technology Library, Vol. 83

Open channel hydraulics has always been a very interesting domain of scienti c and engineering activity because of the great importance of water for human l- ing. The free surface ow, which takes place in the oceans, seas and rivers, can be still regarded as one of the most complex physical processes in the environment. The rst source of dif culties is the proper recognition of physical ow processes and their mathematical description. The second one is related to the solution of the derived equations. The equations arising in hydrodynamics are rather comp- cated and, except some much idealized cases, their solution requires application of the numerical methods. For this reason the great progress in open channel ow modeling that took place during last 40 years paralleled the progress in computer technique, informatics and numerical methods. It is well known that even ty- cal hydraulic engineering problems need applications of computer codes. Thus, we witness a rapid development of ready-made packages, which are widely d- seminated and offered for engineers. However, it seems necessary for their users to be familiar with some fundamentals of numerical methods and computational techniques applied for solving the problems of interest. This is helpful for many r- sons. The ready-made packages can be effectively and safely applied on condition that the users know their possibilities and limitations. For instance, such knowledge is indispensable to distinguish in the obtained solutions the effects coming from the considered physical processes and those caused by numerical artifacts.

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.

Comprehensive coverage of the numerical algorithms applied in open channel modelling, including the standard approaches as well as new schemes developed by the author Step-by-step development from the basic physical equations to the solution of practical problems Provides new insights into numerical solution of some classical problems of open channel hydraulics, e.g. steady varied flow in a channel of arbitrary geometry. Special attention paid to the accuracy analysis of the algorithms allowing for better interpretation of the results obtained with simulation software Includes an in-depth analysis of the simplified flood routing models and their properties