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Numerical modeling in open channel hydraulics (Water science & technology library), 2010 Coll. Water Science and Technology Library, Vol. 83

Langue : Français

Auteur :

Couverture de l’ouvrage Numerical modeling in open channel hydraulics (Water science & technology library)
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.
1. Open channel flow equations. 1.1. Basic definitions. 1.2. General equations for incompressible liquid flow. 1.3. Derivation of 1-D dynamic equation. 1.4. Derivation of 1- D continuity equation. 1.5. System of equations for unsteady gradually varied flow in open channel. 1.6. Steady gradually varied flow in open channel. 1.7. Storage equation. 1.8. Equation of mass transport. 1.9. Thermal energy transport equation. 1.10. Types of equations applied in open channel hydraulics. 2. Methods for solving algebraic equations and their systems. 2.1. Solution of non-linear algebraic equations. 2.2. Solution of systems of the linear algebraic equations. 2.3. Solution of non-linear system of equations. 3. Numerical solution of ordinary differential equations. 3.1. Initial- value problem. 3.2. Initial value problem for a system of ordinary differential equations. 3.3. Boundary value problem. 4. Steady gradually varied flow in open channels. 4.1. Introduction. 4.2. Numerical solution of the initial value problem for steady gradually varied flow equation in a single channel. 4.3. Solution of the boundary problem for steady gradually varied flow equation in single channel. 4.4. Steady gradually varied flow in open channel networks. 5. Partial differential equations of hyperbolic and parabolic type. 5.1. Types of partial differential equations and their properties. 5.2. Introduction to the finite difference method. 5.3. Introduction to the finite element method. 5.4. Properties of the numerical methods for partial differential equations. 6. Numerical solution of the advection equation. 6.1. Solution by the finite difference method. 6.2. Amplitude and phase errors. 6.3. Accuracy analysis using the modified equation approach. 6.4. Solution of the advection equation with the finite element method. 6.5. Numerical solution of the advection equation with the method of characteristics. 7. Numerical solution of the advection- diffusion equation. 7.1. Problem presentation. 7.2. Solution by the finite difference method. 7.3. Solution using the finite element method. 7.4. Solution of the advection- diffusion equation with splitting technique. 7.5. Solution of the advection- diffusion equation using the splitting technique and the convolution integral. 8. Numerical integration of the system of Saint Venant equations. 8.1. Introduction. 8.2. Solution of the Saint Venant equations using the Preissmann scheme. 8.3. Solution of the Saint Venent equations using the modified finite element method. 8.4. Some aspects of application of the Saint Venant equations. 8.5. Unsteady flow in the case of movable channel bed. 8.6. Application of the Saint Venant equations for the steep waves. 9. Simplified equations of the unsteady flow in open channel. 9.1. Simplified forms of the Saint Venant equations. 9.2. Simplified flood routing models in the form of transport equations. 9.3. Mass and momentum conservation in the simplified flood routing models in the form of transport equations. 9.4. Lumped flood routing models. 9.5. Convolution integral in open channel hydraulics.

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

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