Mathematical Models

Mathematical Models

By: Jean-Michel Tanguy (editor)Hardback

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Description

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.

About Author

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.

Contents

Introduction xix Jean-Michel TANGUY Chapter 1. Reminders on the Mechanical Properties of Fluids 1 Jacques GEORGE 1.1. Laws of conservation, principles and general theorems 1 1.2. Enthalpy, rotation, mixing, saturation 13 1.3. Thermodynamic relations, relations of state and laws of behavior 20 1.4. Turbulent flow 26 1.5. Dynamics of geophysical fluids 30 Chapter 2. 3D Navier-Stokes Equations 35 Veronique DUCROCQ 2.1. The continuity hypothesis 35 2.2. Lagrangian description/Eulerian description 36 2.3. The continuity equation 37 2.4. The movement quantity assessment equation 38 2.5. The energy balance equation 41 2.6. The equation of state 41 2.7. Navier-Stokes equations for a fluid in rotation 41 Chapter 3. Models of the Atmosphere 43 Jean COIFFIER 3.1. Introduction 43 3.2. The various simplifications and corresponding models 44 3.3. The equations with various systems of coordinates 56 3.4. Some typical conformal projections 61 3.5. The operational models 67 3.6. Bibliography 69 Chapter 4. Hydrogeologic Models 71 Dominique THIERY 4.1. Equation of fluid mechanics 71 4.2. Continuity equation in porous media 72 4.3. Navier-Stokes' equations 74 4.4. Darcy's law 76 4.5. Calculating mass storage from the equations of state 80 4.6. General equation of hydrodynamics in porous media 82 4.7. Flows in unsaturated media 84 4.8. Bibliography 91 Chapter 5. Fluvial and Maritime Currentology Models 93 Jean-Michel TANGUY 5.1. 3D hydrostatic model 99 5.2. 2D horizontal model for shallow water 107 5.3. 1D models of fluvial flows 119 5.4. Putting 1D models into real time 131 5.5. Bibliography 151 Chapter 6. Urban Hydrology Models 155 Bernard CHOCAT 6.1. Global models and detailed models used in surface flows 156 6.2. Rainfall representation and rainfall-flow transformation 161 6.3. Modeling of the losses into the ground 164 6.4. Transfer function 169 6.5. Modeling of the hydraulic operating conditions of the networks 177 6.6. Production and transport of polluting agents 189 6.7. Conclusion 205 6.8. Bibliography 206 Chapter 7. Tidal Model and Tide Streams 213 Bernard SIMON 7.1. Tidal coefficient 214 7.2. Non-harmonic methods 215 7.3. Compatibilities 216 7.4. Tidal coefficient 222 7.5. Modeling 223 7.6. Tidal currents 226 Chapter 8. Wave Generation and Coastal Current Models 235 Jean-Michel TANGUY, Jean-Michel LEFEVRE and Philippe SERGENT 8.1. Types of swell models 235 8.2. Spectral approach in high waters 242 8.3. Wave generation models 246 8.4. Wave propagation models 260 8.5. Agitating models within the harbors 266 8.6. Non-linear wave model: Boussinesq model 298 8.7. Coastal current models influenced or created by the swell 320 8.8. Bibliography 325 Chapter 9. Solid Transport Models and Evolution of the Seabed 335 Benoit LE GUENNEC and Jean-Michel TANGUY 9.1. Transport due to the overthrust effect 338 9.2. Total load 344 9.3. Bed forms and roughness 344 9.4. Suspension transport 346 9.5. Evolution model of movable beds 357 9.6. Conclusion 364 9.7. Bibliography 364 Chapter 10. Oil Spill Models 371 Pierre DANIEL 10.1. Behavior of hydrocarbons in marine environment 371 10.2. Oil spill drift models 372 10.3. Example: the MOTHY model 375 10.4. Calculation algorithm of the path of polluting particles 378 10.5. Example of a drift prediction map 379 10.6. Bibliography 379 Chapter 11. Conceptual, Empirical and Other Models 381 Christelle ALOT and Florence HABETS 11.1. Evapotranspiration 382 11.2. Bibliography 394 Chapter 12. Reservoir Models in Hydrology 397 Patrick FOURMIGUE and Patrick ARNAUD 12.1. Background 397 12.2. Main principles 399 12.3. Mathematical tools 401 12.4. Forecasting 403 12.5. Integration of the spatial information 405 12.6. Modeling limits 406 12.7. Bibliography 406 Chapter 13. Reservoir Models in Hydrogeology 409 Dominique THIERY 13.1. Principles and objectives 409 13.2. Catchment basin 410 13.3. Setting the model up 411 13.4. Data and parameters 412 13.5. Application domains 412 Chapter 14. Artificial Neural Network Models 419 Anne JOHANNET 14.1. Neural networks: a rapidly changing domain 420 14.2. Neuron and architecture models 422 14.3. How to take into account the non-linearity 429 14.4. Case study: identification of the rainfall-runoff relation of a karst 434 14.5. Acknowledgments 441 14.6. Bibliography 441 Chapter 15. Model Coupling 445 Rachid ABABOU, Denis DARTUS and Jean-Michel TANGUY 15.1. Model coupling 446 15.2. Bibliography 488 Chapter 16. A Set of Hydrological Models 493 Charles PERRIN, Claude MICHEL and Vasken ANDREASSIAN 16.1. Introduction 493 16.2. Description of the annual GR1A rainfall-runoff model 495 16.3. Description of the monthly GR2M rainfall-runoff model 496 16.4. Description of the daily GR4J rainfall-runoff model 500 16.5. Applications of the models 505 16.6. Conclusions and future work 506 16.7. Bibliography 507 List of Authors 511 Index 515 General Index of Authors 517 Summary of the Other Volumes in the Series 519

Product Details

  • ISBN13: 9781848211544
  • Format: Hardback
  • Number Of Pages: 570
  • ID: 9781848211544
  • weight: 1018
  • ISBN10: 1848211546

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  • 1st Class Delivery: Yes
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