Environmental Hydraulics - Numerical Methods

Informationen zum Autor Jean-Michel Tanguy is a French civil engineer who passed a master degree in Ice Hydraulics and a PhD in River Sediment Transport Modelling at Laval University! Quebec. Klappentext This series of five volumes proposes an integrated description of physical processes modeling used by scientific disciplines from meteorology to coastal morphodynamics. Volume 1 describes the physical processes and identifies the main measurement devices used to measure the main parameters that are indispensable to implement all these simulation tools. Volume 2 presents the different theories in an integrated approach: mathematical models as well as conceptual models, used by all disciplines to represent these processes. Volume 3 identifies the main numerical methods used in all these scientific fields to translate mathematical models into numerical tools. Volume 4 is composed of a series of case studies, dedicated to practical applications of these tools in engineering problems. To complete this presentation, volume 5 identifies and describes the modeling software in each discipline. Zusammenfassung This series of five volumes proposes an integrated description of physical processes modeling used by scientific disciplines from meteorology to coastal morphodynamics. Volume 1 describes the physical processes and identifies the main measurement devices used to measure the main parameters that are indispensable to implement all these simulation tools. Volume 2 presents the different theories in an integrated approach: mathematical models as well as conceptual models, used by all disciplines to represent these processes. Volume 3 identifies the main numerical methods used in all these scientific fields to translate mathematical models into numerical tools. Volume 4 is composed of a series of case studies, dedicated to practical applications of these tools in engineering problems. To complete this presentation, volume 5 identifies and describes the modeling software in each discipline. Inhaltsverzeichnis 19773590 ...

List of contents

Introduction xiii

PART 1. GENERAL CONSIDERATIONS CONCERNING NUMERICAL TOOLS 1

Chapter 1. Feedback on the Notion of a Model and the Need for Calibration 3
Denis DARTUS

1.1. "Static" and "dynamic" calibrations of a model 6

1.2. "Dynamic" calibration of a model or data assimilation 10

1.3. Bibliography 10

Chapter 2. Engineering Model and Real-Time Model 11
Jean-Michel TANGUY

2.1. Categories of modeling tools 11

2.2. Weather forecasting at Météo France 12

2.3. Flood forecasting 18

2.4. Characteristics of real-time models 23

2.5. Environment of real-time platforms 25

2.6. Interpretation of hydrological forecasting by those responsible for civil protection 27

2.7. Conclusion 29

2.8. Bibliography 30

Chapter 3. From Mathematical Model to Numerical Model 31
Jean-Michel TANGUY

3.1. Classification of the systems of differential equations 32

3.3. Discrete systems and continuous systems 40

3.4. Equilibrium and propagation problems 41

3.5. Linear and non-linear systems 43

3.6. Conclusion 57

3.7. Bibliography 57

PART 2. DISCRETIZATION METHODS 59

Chapter 4. Problematic Issues Encountered 61
Marie-Madeleine MAUBOURGUET

4.1. Examples of unstable problems 62

4.2. Loss of material 63

4.3. Unsuitable scheme 66

4.4. Bibliography 69

Chapter 5. General Presentation of Numerical Methods 71
Serge PIPERNO and Alexandre ERN

5.1. Introduction 71

5.2. Finite difference method 72

5.3. Finite volume method 77

5.4. Finite element method 78

5.5. Comparison of the different methods on a convection/diffusion problem 92

5.6. Bibliography 93

Chapter 6. Finite Differences 95
Marie-Madeleine MAUBOURGUET and Jean-Michel TANGUY

6.1. General principles of the finite difference method 95

6.2. Discretization of initial and boundary conditions 102

6.3. Resolution on a 2D domain 105

Chapter 7. Introduction to the Finite Element Method 109
Jean-Michel TANGUY

7.1. Elementary FEM concepts and presentation of the section 109

7.2. Method of approximation by finite elements 111

7.3. Geometric transformation 114

7.4. Transformation of derivation and integration operators 121

7.5. Geometric definition of the elements 125

7.6. Method of weighted residuals 128

7.7. Transformation of integral forms 130

7.8. Matrix presentation of the finite element method 133

7.9. Integral form of We on the reference element 140

7.10. Introduction of the Dirichlet-type boundary conditions 148

7.11. Summary: implementation of the finite element method 151

7.12. Application example: wave propagation 151

7.13. Bibliography 158

Chapter 8. Presentation of the Finite Volume Method 161Alexandre ERN and Serge PIPERNO, section 8.6 written by Dominique THIÉRY

8.1. 1D conservation equations 162

8.2. Classical, weak and entropic solutions 170

8.3. Numerical solution of a conservation law 175

8.4. Numerical solution of hyperbolic systems 183

8.5. High-order, finite volume methods 194

8.6. Application of the finite volume method to the flow development of groundwater 195

8.7. Bibliography 210

Chapter 9. Spectral Methods in Meteorology 213
Jean COIFFIER

9.1. Introduction 213

9.2. Using finite series expansion of functions 214

9.3. The spectral method on the sphere 216

9.4. The spectral method on a biperiodic domain 227

9.5. Bibliography 232

Chapter 10. Numerical-Scheme Study 235
Jean-Michel TANGUY

10.1. Reminder of the notion of the numerical scheme 235

10.2. Time discretization 236

10.3. Space discretization 240

10.4. Scheme study: notions of consistency, stability and convergence 241

10.5. Bibliography 264

Chapter 11. Resolution Methods 267
Marie-Madeleine MAUBOURGUET

11.1. Temporal integration methods 268

11.2. Linearization methods for non-linear systems 270

11.3. Methods for solving linear systems AX = B 271

11.4. Bibliography 272

PART 3. INTRODUCTION TO DATA ASSIMILA

About the author

Jean-Michel Tanguy, Ministry of Sustainable Development, France.

Summary

This series of five volumes proposes an integrated description of physical processes modeling used by scientific disciplines from meteorology to coastal morphodynamics.

Report

"An inventory of ground measurement instruments, which provide necessary input data for the various modeling tools described in the book, is drawn up, and mathematical models describing each field within the overall subject area are detailed by a series of system equations." (Live-PR (EN), 19 April 2011)

Product details

• Authors: Tanguy, Jean-Michel Tanguy, JM Tanguy
• Assisted by: Jean-Miche Tanguy (Editor), Jean-Michel Tanguy (Editor)
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 21.06.2010
• EAN: 9781848211551
• ISBN: 978-1-84821-155-1
• Series: ISTE; Environmental Hydraulics; ISTE; Environmental Hydraulics
• Subjects: Natural sciences, medicine, IT, technology > Geosciences; Mathematik, Maschinenbau, Hydrologie, Hydraulik, Geowissenschaften, Strömungsmechanik, Mathematics, Mechanical Engineering, Earth Sciences, Fluid mechanics, Applied Mathematics in Science, Mathematik in den Naturwissenschaften, Hydrological Sciences