Vincent Guinot,
V Guinot
John Wiley & Sons
2e druk, 2010
9781848212138
Wave Propagation in Fluids, 2nd Edition
Models and Numerical Techniques
Specificaties
Gebonden, 558 blz.
|
Engels
John Wiley & Sons |
2e druk, 2010
ISBN13: 9781848212138
Rubricering
Onderdeel van serie
ISTE
Verwachte levertijd ongeveer 16 werkdagen
Samenvatting
This second edition with four additional chapters presents the physical principles and solution techniques for transient propagation in fluid mechanics and hydraulics. The application domains vary including contaminant transport with or without sorption, the motion of immiscible hydrocarbons in aquifers, pipe transients, open channel and shallow water flow, and compressible gas dynamics.
The mathematical formulation is covered from the angle of conservation laws, with an emphasis on multidimensional problems and discontinuous flows, such as steep fronts and shock waves.
Finite difference–, finite volume– and finite element–based numerical methods (including discontinuous Galerkin techniques) are covered and applied to various physical fields. Additional chapters include the treatment of geometric source terms, as well as direct and adjoint sensitivity modeling for hyperbolic conservation laws. A concluding chapter is devoted to practical recommendations to the modeler.
Application exercises with on–line solutions are proposed at the end of the chapters.
Specificaties
ISBN13:9781848212138
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:558
Uitgever:John Wiley & Sons
Druk:2
Serie:ISTE
Inhoudsopgave
<p>Introduction xv</p>
<p>Chapter 1. Scalar Hyperbolic Conservation Laws in One Dimension of Space 1</p>
<p>1.1. Definitions 1</p>
<p>1.2. Determination of the solution 9</p>
<p>1.3. A linear law: the advection equation 14</p>
<p>1.4. A convex law: the inviscid Burgers equation 21</p>
<p>1.5. Another convex law: the kinematic wave for free–surface hydraulics 28</p>
<p>1.6. A non–convex conservation law: the Buckley–Leverett equation 35</p>
<p>1.7. Advection with adsorption/desorption 42</p>
<p>1.8. Summary of Chapter 1 47</p>
<p>Chapter 2. Hyperbolic Systems of Conservation Laws in One Dimension of Space 53</p>
<p>2.1. Definitions 53</p>
<p>2.2. Determination of the solution 59</p>
<p>2.3. A particular case: compressible flows 63</p>
<p>2.4. A linear 2×2 system: the water hammer equations 68</p>
<p>2.5. A nonlinear 2×2 system: the Saint Venant equations 84</p>
<p>2.6. A nonlinear 3×3 system: the Euler equations 108</p>
<p>2.7. Summary of Chapter 2 122</p>
<p>Chapter 3. Weak Solutions and their Properties 131</p>
<p>3.1. Appearance of discontinuous solutions 131</p>
<p>3.2. Classification of waves 138</p>
<p>3.3. Simple waves 142</p>
<p>3.4. Weak solutions and their properties 144</p>
<p>3.5. Summary 157</p>
<p>Chapter 4. The Riemann Problem 161</p>
<p>4.1. Definitions solution properties 161</p>
<p>4.2. Solution for scalar conservation laws 165</p>
<p>4.3. Solution for hyperbolic systems of conservation laws 173</p>
<p>4.4. Summary 189</p>
<p>Chapter 5. Multidimensional Hyperbolic Systems 193</p>
<p>5.1. Definitions 193</p>
<p>5.2. Derivation from conservation principles 197</p>
<p>5.3. Solution properties 200</p>
<p>5.4. Application: the two–dimensional shallow water equations 208</p>
<p>5.5. Summary 221</p>
<p>Chapter 6. Finite Difference Methods for Hyperbolic Systems 223</p>
<p>6.1. Discretization of time and space 223</p>
<p>6.2. The method of characteristics (MOC) 227</p>
<p>6.3. Upwind schemes for scalar laws 244</p>
<p>6.4. The Preissmann scheme 250</p>
<p>6.5. Centered schemes 260</p>
<p>6.6. TVD schemes 263</p>
<p>6.7. The flux splitting technique 271</p>
<p>6.8. Conservative discretizations: Roe s matrix 280</p>
<p>6.9. Multidimensional problems 284</p>
<p>6.10. Summary 289</p>
<p>Chapter 7. Finite Volume Methods for Hyperbolic Systems 293</p>
<p>7.1. Principle 293</p>
<p>7.2. Godunov s scheme 299</p>
<p>7.3. Higher–order Godunov–type schemes 313</p>
<p>7.4. EVR approach 319</p>
<p>7.5. Summary 326</p>
<p>Chapter 8. Finite Element Methods for Hyperbolic Systems 329</p>
<p>8.1. Principle for one–dimensional scalar laws 329</p>
<p>8.2. One–dimensional hyperbolic systems 340</p>
<p>8.3. Extension to multidimensional problems 344</p>
<p>8.4. Discontinuous Galerkin techniques 347</p>
<p>8.5. Application examples 354</p>
<p>8.6. Summary 368</p>
<p>Chapter 9. Treatment of Source Terms 371</p>
<p>9.1. Introduction 371</p>
<p>9.2. Problem position 372</p>
<p>9.3. Source term upwinding techniques 377</p>
<p>9.4. The quasi–steady wave algorithm 386</p>
<p>9.5. Balancing techniques 390</p>
<p>9.6. Computational example 403</p>
<p>9.7. Summary 408</p>
<p>Chapter 10. Sensitivity Equations for Hyperbolic Systems 411</p>
<p>10.1. Introduction 411</p>
<p>10.2. Forward sensitivity equations for scalar laws 413</p>
<p>10.3. Forward sensitivity equations for hyperbolic systems 422</p>
<p>10.4. Adjoint sensitivity equations 435</p>
<p>10.5. Finite volume solution of the forward sensitivity equations 441</p>
<p>10.6. Summary 447</p>
<p>Chapter 11. Modeling in Practice 449</p>
<p>11.1. Modeling software 449</p>
<p>11.2. Mesh quality 454</p>
<p>11.3. Boundary conditions 459</p>
<p>11.4. Numerical parameters 464</p>
<p>11.5. Simplifications in the governing equations 466</p>
<p>11.6. Numerical solution assessment 472</p>
<p>11.7. Getting started with a simulation package 477</p>
<p>Appendix A. Linear Algebra 479</p>
<p>Appendix B. Numerical Analysis 487</p>
<p>Appendix C. Approximate Riemann Solvers 505</p>
<p>Appendix D. Summary of the Formulae 521</p>
<p>Bibliography 527</p>
<p>Index 537</p>
<p>Chapter 1. Scalar Hyperbolic Conservation Laws in One Dimension of Space 1</p>
<p>1.1. Definitions 1</p>
<p>1.2. Determination of the solution 9</p>
<p>1.3. A linear law: the advection equation 14</p>
<p>1.4. A convex law: the inviscid Burgers equation 21</p>
<p>1.5. Another convex law: the kinematic wave for free–surface hydraulics 28</p>
<p>1.6. A non–convex conservation law: the Buckley–Leverett equation 35</p>
<p>1.7. Advection with adsorption/desorption 42</p>
<p>1.8. Summary of Chapter 1 47</p>
<p>Chapter 2. Hyperbolic Systems of Conservation Laws in One Dimension of Space 53</p>
<p>2.1. Definitions 53</p>
<p>2.2. Determination of the solution 59</p>
<p>2.3. A particular case: compressible flows 63</p>
<p>2.4. A linear 2×2 system: the water hammer equations 68</p>
<p>2.5. A nonlinear 2×2 system: the Saint Venant equations 84</p>
<p>2.6. A nonlinear 3×3 system: the Euler equations 108</p>
<p>2.7. Summary of Chapter 2 122</p>
<p>Chapter 3. Weak Solutions and their Properties 131</p>
<p>3.1. Appearance of discontinuous solutions 131</p>
<p>3.2. Classification of waves 138</p>
<p>3.3. Simple waves 142</p>
<p>3.4. Weak solutions and their properties 144</p>
<p>3.5. Summary 157</p>
<p>Chapter 4. The Riemann Problem 161</p>
<p>4.1. Definitions solution properties 161</p>
<p>4.2. Solution for scalar conservation laws 165</p>
<p>4.3. Solution for hyperbolic systems of conservation laws 173</p>
<p>4.4. Summary 189</p>
<p>Chapter 5. Multidimensional Hyperbolic Systems 193</p>
<p>5.1. Definitions 193</p>
<p>5.2. Derivation from conservation principles 197</p>
<p>5.3. Solution properties 200</p>
<p>5.4. Application: the two–dimensional shallow water equations 208</p>
<p>5.5. Summary 221</p>
<p>Chapter 6. Finite Difference Methods for Hyperbolic Systems 223</p>
<p>6.1. Discretization of time and space 223</p>
<p>6.2. The method of characteristics (MOC) 227</p>
<p>6.3. Upwind schemes for scalar laws 244</p>
<p>6.4. The Preissmann scheme 250</p>
<p>6.5. Centered schemes 260</p>
<p>6.6. TVD schemes 263</p>
<p>6.7. The flux splitting technique 271</p>
<p>6.8. Conservative discretizations: Roe s matrix 280</p>
<p>6.9. Multidimensional problems 284</p>
<p>6.10. Summary 289</p>
<p>Chapter 7. Finite Volume Methods for Hyperbolic Systems 293</p>
<p>7.1. Principle 293</p>
<p>7.2. Godunov s scheme 299</p>
<p>7.3. Higher–order Godunov–type schemes 313</p>
<p>7.4. EVR approach 319</p>
<p>7.5. Summary 326</p>
<p>Chapter 8. Finite Element Methods for Hyperbolic Systems 329</p>
<p>8.1. Principle for one–dimensional scalar laws 329</p>
<p>8.2. One–dimensional hyperbolic systems 340</p>
<p>8.3. Extension to multidimensional problems 344</p>
<p>8.4. Discontinuous Galerkin techniques 347</p>
<p>8.5. Application examples 354</p>
<p>8.6. Summary 368</p>
<p>Chapter 9. Treatment of Source Terms 371</p>
<p>9.1. Introduction 371</p>
<p>9.2. Problem position 372</p>
<p>9.3. Source term upwinding techniques 377</p>
<p>9.4. The quasi–steady wave algorithm 386</p>
<p>9.5. Balancing techniques 390</p>
<p>9.6. Computational example 403</p>
<p>9.7. Summary 408</p>
<p>Chapter 10. Sensitivity Equations for Hyperbolic Systems 411</p>
<p>10.1. Introduction 411</p>
<p>10.2. Forward sensitivity equations for scalar laws 413</p>
<p>10.3. Forward sensitivity equations for hyperbolic systems 422</p>
<p>10.4. Adjoint sensitivity equations 435</p>
<p>10.5. Finite volume solution of the forward sensitivity equations 441</p>
<p>10.6. Summary 447</p>
<p>Chapter 11. Modeling in Practice 449</p>
<p>11.1. Modeling software 449</p>
<p>11.2. Mesh quality 454</p>
<p>11.3. Boundary conditions 459</p>
<p>11.4. Numerical parameters 464</p>
<p>11.5. Simplifications in the governing equations 466</p>
<p>11.6. Numerical solution assessment 472</p>
<p>11.7. Getting started with a simulation package 477</p>
<p>Appendix A. Linear Algebra 479</p>
<p>Appendix B. Numerical Analysis 487</p>
<p>Appendix C. Approximate Riemann Solvers 505</p>
<p>Appendix D. Summary of the Formulae 521</p>
<p>Bibliography 527</p>
<p>Index 537</p>