Wave Propagation in Fluids

Vincent Guinot is professor of hydrodynamic modeling at the University of Montpellier, France. He teaches fluid mechanics, hydraulics, numerical methods and hydrodynamic modeling.

• Introduction  xvChapter 1. Scalar Hyperbolic Conservation Laws in One Dimension of Space 11.1. Definitions 11.2. Determination of the solution 91.3. A linear law: the advection equation 141.4. A convex law: the inviscid Burgers equation 211.5. Another convex law: the kinematic wave for free-surface hydraulics 281.6. A non-convex conservation law: the Buckley-Leverett equation 351.7. Advection with adsorption/desorption 421.8. Summary of Chapter 1 47Chapter 2. Hyperbolic Systems of Conservation Laws in One Dimension of Space 532.1. Definitions 532.2. Determination of the solution 592.3. A particular case: compressible flows 632.4. A linear 2×2 system: the water hammer equations 682.5. A nonlinear 2×2 system: the Saint Venant equations 842.6. A nonlinear 3×3 system: the Euler equations 1082.7. Summary of Chapter 2 122Chapter 3. Weak Solutions and their Properties 1313.1. Appearance of discontinuous solutions 1313.2. Classification of waves 1383.3. Simple waves 1423.4. Weak solutions and their properties 1443.5. Summary 157Chapter 4. The Riemann Problem 1614.1. Definitions – solution properties 1614.2. Solution for scalar conservation laws 1654.3. Solution for hyperbolic systems of conservation laws 1734.4. Summary 189Chapter 5. Multidimensional Hyperbolic Systems 1935.1. Definitions 1935.2. Derivation from conservation principles 1975.3. Solution properties 2005.4. Application: the two-dimensional shallow water equations 2085.5. Summary 221Chapter 6. Finite Difference Methods for Hyperbolic Systems 2236.1. Discretization of time and space 2236.2. The method of characteristics (MOC) 2276.3. Upwind schemes for scalar laws 2446.4. The Preissmann scheme 2506.5. Centered schemes 2606.6. TVD schemes 2636.7. The flux splitting technique 2716.8. Conservative discretizations: Roe’s matrix 2806.9. Multidimensional problems 2846.10. Summary 289Chapter 7. Finite Volume Methods for Hyperbolic Systems 2937.1. Principle 2937.2. Godunov’s scheme 2997.3. Higher-order Godunov-type schemes 3137.4. EVR approach 3197.5. Summary 326Chapter 8. Finite Element Methods for Hyperbolic Systems 3298.1. Principle for one-dimensional scalar laws 3298.2. One-dimensional hyperbolic systems 3408.3. Extension to multidimensional problems 3448.4. Discontinuous Galerkin techniques 3478.5. Application examples 3548.6. Summary 368Chapter 9. Treatment of Source Terms 3719.1. Introduction 3719.2. Problem position 3729.3. Source term upwinding techniques 3779.4. The quasi-steady wave algorithm 3869.5. Balancing techniques 3909.6. Computational example 4039.7. Summary 408Chapter 10. Sensitivity Equations for Hyperbolic Systems 41110.1. Introduction 41110.2. Forward sensitivity equations for scalar laws 41310.3. Forward sensitivity equations for hyperbolic systems 42210.4. Adjoint sensitivity equations 43510.5. Finite volume solution of the forward sensitivity equations 44110.6. Summary 447Chapter 11. Modeling in Practice 44911.1. Modeling software 44911.2. Mesh quality 45411.3. Boundary conditions 45911.4. Numerical parameters 46411.5. Simplifications in the governing equations 46611.6. Numerical solution assessment 47211.7. Getting started with a simulation package 477Appendix A. Linear Algebra 479Appendix B. Numerical Analysis 487Appendix C. Approximate Riemann Solvers 505Appendix D. Summary of the Formulae 521Bibliography 527Index 537

"However, for practitioners this book can give an insight into physical phenomena of wave propagation in fluids." (Zentralblatt MATH, 2011)