Additional Information
Book Details
Abstract
Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. It provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment. Flow equations, numerical and analytical solutions are included. The necessary steps for building and applying numerical methods in hydraulics comprise the core of the book and this is followed by a report of different example applications of computational hydraulics: river training effects on flood propagation, water quality modelling of lakes and coastal applications. The theory and exercises included in the book promote learning of concepts within academic environments.
Sample codes are made available online for purchasers of the book. Computational Hydraulics is intended for under-graduate and graduate students, researchers, members of governmental and non-governmental agencies and professionals involved in management of the water related problems.
Author: Ioana Popescu, Hydroinformatics group, UNESCO-IHE Institute for Water Education, Delft , The Netherlands.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover\r | Cover | ||
| Contents\r | v | ||
| About the author | ix | ||
| Preface | xi | ||
| Chapter 1: Modelling theory | 1 | ||
| 1.1 Context and Nature of Modelling | 1 | ||
| 1.1.1 Classification of models\r | 2 | ||
| 1.1.2 Computational Hydraulics\r | 5 | ||
| 1.2 Conceptualiation: Buiding a Model\r | 6 | ||
| 1.3 Mathematical Modelling in Practice\r | 7 | ||
| 1.3.1 Selecting a proper model\r | 7 | ||
| 1.3.2 Testing a model\r | 8 | ||
| 1.4 Development and Application of Models\r | 9 | ||
| Chapter 2:\rModelling water related problems | 11 | ||
| 2.1 Basic Conservation Equations\r | 11 | ||
| 2.1.1 Conservation of mass\r | 12 | ||
| 2.1.2 Conservation of momentum\r | 13 | ||
| 2.1.3 Conservation of energy\r | 15 | ||
| 2.2 Mathematical Classification of Flow Equations\r | 15 | ||
| 2.2.1 Solutions of ODE\r | 17 | ||
| 2.2.2 Solutions of PDE\r | 17 | ||
| 2.2.2.1\rBoundary conditions for fluid flows PDEs | 18 | ||
| 2.2.2.2\rHyperbolic equation examples | 20 | ||
| 2.2.2.3\rParabolic equation example | 22 | ||
| 2.2.2.4 Elliptic equation example\r | 23 | ||
| 2.3 Navier-Stokes and Saint-Venant Equations\r | 24 | ||
| 2.3.1 Navier-Stokes equations\r | 24 | ||
| 2.3.2 Saint-Venant equations\r | 25 | ||
| 2.3.2.1 Kinematic wave solution\r | 27 | ||
| 2.3.2.2 Diffusive wave solution\r | 28 | ||
| 2.3.2.3 Fully dynamic wave solution\r | 29 | ||
| 2.3.3 Characteristic form of Saint-Venant equations\r | 29 | ||
| Chapter 3:\rDiscretization of the fluid flow domain | 33 | ||
| 3.1 Discrete Solutions of Equations\r | 33 | ||
| 3.2 Space Discretization\r | 36 | ||
| 3.2.1 Structured grids\r | 36 | ||
| 3.2.2 Unstructured grids\r | 38 | ||
| 3.2.3 Grid generation\r | 39 | ||
| 3.2.4 Physical aspects of space discretization\r | 40 | ||
| 3.3 Time Discretization\r | 41 | ||
| Chapter 4:\rFinite difference method | 43 | ||
| 4.1 General Concepts\r | 43 | ||
| 4.2 Approximation of the First Order Derrivative\r | 44 | ||
| 4.3 Approximation of Higher Order Derrivatives\r | 48 | ||
| 4.4 Finite Differences for Ordinary Differential Equations\r | 50 | ||
| 4.4.1. Problem position\r | 50 | ||
| 4.4.2. Explicit schemes (Euler method)\r | 52 | ||
| 4.4.3. Implicit schemes (Improved euler method)\r | 53 | ||
| 4.4.4 Mixed schemes\r | 53 | ||
| 4.4.5 Weighted averaged schemes\r | 53 | ||
| 4.4.6. Runge-Kutta methods\r | 55 | ||
| 4.5. Numerical Schemes for Partial Differential Equations\r | 56 | ||
| 4.5.1. Principle of FDM for PDEs\r | 56 | ||
| 4.5.2 Hyperbolic PDEs\r | 59 | ||
| 4.5.2.1. Explicit and implicit schemes\r | 59 | ||
| 4.5.2.2 Forward time – centered space scheme (FTCS)\r | 60 | ||
| 4.5.2.3. Centered and upwind schemes\r | 61 | ||
| 4.5.2.4. The preissmann scheme\r | 61 | ||
| 4.5.2.5. The abbott-ionescu scheme for free-surface flow\r | 63 | ||
| 4.5.3. Parabolic PDEs\r | 65 | ||
| 4.5.3.1. Explicit schemes\r | 65 | ||
| 4.5.3.2. Implicit scheme\r | 67 | ||
| 4.5.4. Elliptic PDEs\r | 67 | ||
| 4.6. Examples\r | 68 | ||
| 4.6.1.\rODE: Solution of the linear reservoir problem | 68 | ||
| 4.6.2. PDE: Simple wave propagation\r | 72 | ||
| 4.6.3.\rPDE: Diffusion equation | 74 | ||
| Chapter 5:\rFinite volume method | 77 | ||
| 5.1 General Concept\r | 77 | ||
| 5.2 FVM Application Details\r | 80 | ||
| 5.2.1 Step by step application of the FVM\r | 80 | ||
| 5.2.2 Surface and volume integrals\r | 81 | ||
| 5.2.3 Discretisation of convective fluxes\r | 83 | ||
| 5.2.3.1 Upwind Approach\r | 83 | ||
| 5.2.3.2 Central Differences\r | 85 | ||
| 5.2.4 Discretisation of diffusive fluxes\r | 85 | ||
| 5.2.5 Evaluation of the time derivative\r | 86 | ||
| 5.2.6 Boundary conditions\r | 86 | ||
| 5.2.4 Solving algebraic system of equations\r | 86 | ||
| 5.3 Example of the Advection Diffusion Equation in 1-D\r | 88 | ||
| 5.3.1 Constant unknown function\r | 90 | ||
| 5.3.2 Linear variation approximation of the unknown function\r | 91 | ||
| 5.3.3 Parabolic variation approximation of the unknown function\r | 91 | ||
| 5.3.4 Error of the approximation\r | 92 | ||
| Chapter 6:\rProperties of numerical methods | 95 | ||
| 6.1 Properties of Numerical Methods\r | 95 | ||
| 6.1.1 Convergence\r | 95 | ||
| 6.1.2 Consistency\r | 96 | ||
| 6.1.3 Stability\r | 96 | ||
| 6.1.4 Lax’s theorem of equivalence\r | 97 | ||
| 6.2 Convergence of FDM Schemes\r | 97 | ||
| 6.2.1 Convergence for ODEs\r | 97 | ||
| 6.2.1.1 Consistency\r | 97 | ||
| 6.2.1.2 Stability\r | 99 | ||
| 6.2.2 Convergence for PDEs\r | 101 | ||
| 6.2.2.1 Consistency for PDE\r | 103 | ||
| 6.2.2.2 Stability for PDE\r | 104 | ||
| 6.2.2.3 Numerical diffusion and dispersion\r | 108 | ||
| 6.2.3 Amplitude and phase errors\r | 109 | ||
| 6.3 Convergence of FVM Schemes\r | 111 | ||
| 6.3.1 Convective fluxes\r | 111 | ||
| 6.3.2 Diffusive fluxes\r | 112 | ||
| 6.4 Examples\r | 113 | ||
| 6.4.1 Stability region of a simple ODE\r | 113 | ||
| 6.4.2\rConvergence of an ODE: emptying of a groundwater reservoir | 113 | ||
| 6.4.2.1\rExplicit schemes | 114 | ||
| 6.4.2.2\rImplicit schemes | 117 | ||
| 6.4.3\rPDE: Convergence analysis for Preissmann scheme applied \rto advection equation | 117 | ||
| 6.4.4\rPDE: Convergence analysis for diffusion equation | 123 | ||
| Chapter 7:\rRiver system modelling and floodpropagation | 125 | ||
| 7.1 Introduction\r | 125 | ||
| 7.2 River Systems Modelling\r | 126 | ||
| 7.2.1 Preissmann solution\r | 127 | ||
| 7.2.2 Abbott –ionescu solution\r | 133 | ||
| 7.2.3 Initial and boundary conditions\r | 137 | ||
| 7.2.4 River networks\r | 137 | ||
| 7.3 Modelling Floods\r | 140 | ||
| 7.4 River Routing Example\r | 142 | ||
| Chapter 8:\rWater quality modelling | 147 | ||
| 8.1 Introduction\r | 147 | ||
| 8.2 Processes Described in Water Quality Models\r | 149 | ||
| 8.3 River Water Quality Models\r | 151 | ||
| 8.4 Lakes Water Quality Modelling\r | 152 | ||
| 8.5 Examples of Lake Hydrodynamics and Water Quality Models\r | 154 | ||
| 8.5.1\rSontea-Fortuna wetland system | 154 | ||
| 8.5.2\rLake Taihu water quality | 156 | ||
| References | 161 | ||
| Index | 167 |