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** Mathematical Modeling in Science and Engineering - Ismael Herrera - Audiovisuell/Multimedia (9781118207239) **

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Audiovisuell/Multimedia

Utgitt:

2012

Forlag:

John Wiley & Sons Inc

Språk:

Engelsk

Sider:

224

Format:

25 x 15 cm

ISBN:

9781118207239

This text examines the axiomatic approach, a powerful, unified approach to mathematical and computational modeling in science and engineering. Readers will discover that this axiomatic approach enables them to both systematically construct effective models, and also apply these models to any macroscopic physical system. It is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.

Mathematical Modeling in Science and Engineering

This text examines the axiomatic approach, a powerful, unified approach to mathematical and computational modeling in science and engineering. Readers will discover that this axiomatic approach enables them to both systematically construct effective models, and also apply these models to any macroscopic physical system. It is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.Preface xiii 1 AXIOMATIC FORMULATION OF THE BASIC MODELS 1 1.1 Models 1 1.2 Microscopic and macroscopic physics 2 1.3 Kinematics of continuous systems 3 1.3.1 Intensive properties 6 1.3.2 Extensive properties 8 1.4 Balance equations of extensive and intensive properties 9 1.4.1 Global balance equations 9 1.4.2 The local balance equations 10 1.4.3 The role of balance conditions in the modeling of continuous systems 13 1.4.4 Formulation of motion restrictions by means of balance equations 14 1.5 Summary 16 2 MECHANICS OF CLASSICAL CONTINUOUS SYSTEMS 23 2.1 One-phase systems 23 2.2 The basic mathematical model of one-phase systems 24 2.3 The extensive/intensive properties of classical mechanics 25 2.4 Mass conservation 26 2.5 Linear momentum balance 27 2.6 Angular momentum balance 29 2.7 Energy concepts 32 2.8 The balance of kinetic energy 33 2.9 The balance of internal energy 34 2.10 Heat equivalent of mechanical work 35 2.11 Summary of basic equations for solid and fluid mechanics 35 2.12 Some basic concepts of thermodynamics 36 2.12.1 Heat transport 36 2.13 Summary 38 3 MECHANICS OF NON-CLASSICAL CONTINUOUS SYSTEMS 45 3.1 Multiphase systems 45 3.2 The basic mathematical model of multiphase systems 46 3.3 Solute transport in a free fluid 47 3.4 Transport by fluids in porous media 49 3.5 Flow of fluids through porous media 51 3.6 Petroleum reservoirs: the black-oil model 52 3.6.1 Assumptions of the black-oil model 53 3.6.2 Notation 53 3.6.3 Family of extensive properties 54 3.6.4 Differential equations and jump conditions 55 3.7 Summary 57 4 SOLUTE TRANSPORT BY A FREE FLUID 63 4.1 The general equation of solute transport by a free fluid 64 4.2 Transport processes 65 4.2.1 Advection 65 4.2.2 Diffusion processes 65 4.3 Mass generation processes 66 4.4 Differential equations of diffusive transport 67 4.5 Well-posed problems for diffusive transport 69 4.5.1 Time-dependent problems 70 4.5.2 Steady state 71 4.6 First-order irreversible processes 71 4.7 Differential equations of non-diffusive transport 73 4.8 Well-posed problems for non-diffusive transport 73 4.8.1 Well-posed problems in one spatial dimension 74 4.8.2 Well-posed problems in several spatial dimensions 79 4.8.3 Well-posed problems for steady-state models 80 4.9 Summary 80 5 FLOW OF A FLUID IN A POROUS MEDIUM 85 5.1 Basic assumptions of the flow model 85 5.2 The basic model for the flow of a fluid through a porous medium 86 5.3 Modeling the elasticity and compressibility 87 5.3.1 Fluid compressibility 87 5.3.2 Pore compressibility 88 5.3.3 The storage coefficient 90 5.4 Darcy's law 90 5.5 Piezometric level 92 5.6 General equation governing flow through a porous medium 94 5.6.1 Special forms of the governing differential equation 95 5.7 Applications of the jump conditions 96 5.8 Well-posed problems 96 5.8.1 Steady-state models 97 5.8.2 Time-dependent problems 99 5.9 Models with a reduced number of spatial dimensions 99 5.9.1 Theoretical derivation of a 2-D model for a confined aquifer 100 5.9.2 Leaky aquitard method 102 5.9.3 The integrodifferential equations approach 104 5.9.4 Other 2-D aquifer models 108 5.10 Summary 111 6 SOLUTE TRANSPORT IN A POROUS MEDIUM 117 6.1 Transport processes 118 6.1.1 Advection 118 6.2 Non-conservative processes 118 6.2.1 First-order irreversible processes 119 6.2.2 Adsorption 119 6.3 Dispersion-diffusion 121 6.4 The equations for transport of solutes in porous media 123 6.5 Well-posed problems 125 6

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Mathematical Modeling in Science and Engineering

This text examines the axiomatic approach, a powerful, unified approach to mathematical and computational modeling in science and engineering. Readers will discover that this axiomatic approach enable... Les mer