Computational hydraulics : numerical methods and modelling / Ioana Popescu.

Format:

Book

Author/Creator:

Popescu, Ioana, author.

Language:

English

Subjects (All):

Hydraulics--Mathematics.

Hydraulics.

Hydraulics--Data processing.

Physical Description:

1 online resource (184 p.)

Edition:

1st ed.

Place of Publication:

IWA Publishing 2014

London, England : IWA Publishing, 2014.

Language Note:

English

Summary:

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.

Contents:

Cover

Copyright

Contents

About the author

Preface

Chapter 1: Modelling theory

1.1 Context and Nature of Modelling

1.1.1 Classification of models

1.1.2 Computational Hydraulics

1.2 Conceptualiation: Building a Model

1.3 Mathematical Modelling in Practice

1.3.1 Selecting a proper model

1.3.2 Testing a model

1.4 Development and Application of Models

Chapter 2: Modelling water related problems

2.1 Basic Conservation Equations

2.1.1 Conservation of mass

2.1.2 Conservation of momentum

2.1.3 Conservation of energy

2.2 Mathematical Classification of Flow Equations

2.2.1 Solutions of ODE

2.2.2 Solutions of PDE

2.3 Navier-Stokes and Saint-Venant Equations

2.3.1 Navier-Stokes equations

2.3.2 Saint-Venant equations

2.3.3 Characteristic form of Saint-Venant equations

Chapter 3: Discretization of the fluid flow domain

3.1 Discrete Solutions of Equations

3.2 Space Discretization

3.2.1 Structured grids

3.2.2 Unstructured grids

3.2.3 Grid generation

3.2.4 Physical aspects of space discretization

3.3 Time Discretization

Chapter 4: Finite difference method

4.1 General Concepts

4.2 Approximation of the First Order Derrivative

4.3 Approximation of Higher Order Derrivatives

4.4 Finite Differences for Ordinary Differential Equations

4.4.1 Problem position

4.4.2 Explicit schemes (Euler method)

4.4.3 Implicit schemes (Improved Euler method)

4.4.4 Mixed schemes

4.4.5 Weighted averaged schemes

4.4.6 Runge-Kutta methods

4.5 Numerical Schemes for Partial Differential Equations

4.5.1 Principle of FDM for PDEs

4.5.2 Hyperbolic PDEs

4.5.3 Parabolic PDEs

4.5.4 Elliptic PDEs

4.6 Examples

4.6.1 ODE: Solution of the linear reservoir problem

4.6.2 PDE: Simple wave propagation

4.6.3 PDE: Diffusion equation.

Chapter 5: Finite volume method

5.1 General Concept

5.2 FVM Application Details

5.2.1 Step by step application of the FVM

5.2.2 Surface and volume integrals

5.2.3 Discretization of convective fluxes

5.2.4 Discretization of diffusive fluxes

5.2.5 Evaluation of the time derivative

5.2.6 Boundary conditions

5.2.7 Solving algebraic system of equations

5.3 Example of Advection-Diffusion Equation in 1D

5.3.1 Constant unknown function

5.3.2 Linear variation approximation of the unknown function

5.3.3 Parabolic variation approximation of the unknown function

5.3.4 Error of the approximation

Chapter 6: Properties of numerical methods

6.1 Properties of Numerical Methods

6.1.1 Convergence

6.1.2 Consistency

6.1.3 Stability

6.1.4 Lax's theorem of equivalence

6.2 Convergence of FDM Schemes

6.2.1 Convergence for ODEs

6.2.2 Convergence for PDEs

6.2.3 Amplitude and phase errors

6.3 Convergence of FVM Schemes

6.3.1 Convective fluxes

6.3.2 Diffusive fluxes

6.4 Examples

6.4.1 Stability region of a simple ODE

6.4.2 Convergence of an ODE: Emptying of a groundwater reservoir

6.4.3 PDE: Convergence analysis for Preissmann scheme applied to advection equation

6.4.4 PDE: Convergence analysis for diffusion equation

Chapter 7: River system modelling and flood propagation

7.1 Introduction

7.2 River Systems Modelling

7.2.1 Preissmann solution

7.2.2 Abbott-Ionescu solution

7.2.3 Initial and boundary conditions

7.2.4 River networks

7.3 Modelling Floods

7.4 River Routing Example

Chapter 8: Water quality modelling

8.1 Introduction

8.2 Processes Described in Water Quality Models

8.3 River Water Quality Models

8.4 Lakes Water Quality Modelling

8.5 Examples of Lake Hydrodynamics and Water Quality Models

8.5.1 Sontea-Fortuna wetland system.

8.5.2 Lake Taihu water quality

References

Index.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

CC BY-NC-ND

Description based on online resource; title from PDF title page (ebrary, viewed December 18, 2014).

ISBN:

9781780400457

1780400454

OCLC:

897838585

Access Restriction:

Open access Unrestricted online access