Numerical Modeling in Open Channel Hydraulics

Preface 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 systems2.1. 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 equation 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 Index