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Informationen zum Autor Vincent Guinot is professor of hydrodynamic modeling at the University of Montpellier, France. He teaches fluid mechanics, hydraulics, numerical methods and hydrodynamic modeling. Klappentext This book presents the physical principles of wave propagation in fluid mechanics and hydraulics. The mathematical techniques that allow the behavior of the waves to be analyzed are presented, along with existing numerical methods for the simulation of wave propagation. Particular attention is paid to discontinuous flows, such as steep fronts and shock waves, and their mathematical treatment. A number of practical examples are taken from various areas fluid mechanics and hydraulics, such as contaminant transport, the motion of immiscible hydrocarbons in aquifers, river flow, pipe transients and gas dynamics. Finite difference methods and finite volume methods are analyzed and applied to practical situations, with particular attention being given to their advantages and disadvantages. Application exercises are given at the end of each chapter, enabling readers to test their understanding of the subject. Zusammenfassung This book presents the physical principles of wave propagation in fluid mechanics and hydraulics. The mathematical techniques that allow the behavior of the waves to be analyzed are presented! along with existing numerical methods for the simulation of wave propagation. Inhaltsverzeichnis Introduction xv Chapter 1. Scalar Hyperbolic Conservation Laws in One Dimension of Space 1 1.1. Definitions 1 1.1.1. Hyperbolic scalar conservation laws 1 1.1.2. Derivation from general conservation principles 3 1.1.3. Non-conservation form 6 1.1.4. Characteristic form - Riemann invariants 7 1.2. Determination of the solution 9 1.2.1. Representation in the phase space 9 1.2.2. Initial conditions, boundary conditions 12 1.3. A linear law: the advection equation 14 1.3.1. Physical context - conservation form 14 1.3.2. Characteristic form 16 1.3.3. Example: movement of a contaminant in a river 17 1.3.4. Summary 21 1.4. A convex law: the inviscid Burgers equation 21 1.4.1. Physical context - conservation form 21 1.4.2. Characteristic form 23 1.4.3. Example: propagation of a perturbation in a fluid 24 1.4.4. Summary 28 1.5. Another convex law: the kinematic wave for free-surface hydraulics 28 1.5.1. Physical context - conservation form 28 1.5.2. Non-conservation and characteristic forms 29 1.5.3. Expression of the celerity 31 1.5.4. Specific case: flow in a rectangular channel 34 1.5.5. Summary 35 1.6. A non-convex conservation law: the Buckley-Leverett equation 36 1.6.1. Physical context - conservation form 36 1.6.2. Characteristic form 39 1.6.3. Example: decontamination of an aquifer 40 1.6.4. Summary 42 1.7. Advection with adsorption/desorption 42 1.7.1. Physical context - conservation form 42 1.7.2. Characteristic form 45 1.7.3. Summary 47 1.8. Conclusions 48 1.8.1. What you should remember 48 1.8.2. Application exercises 48 Chapter 2. Hyperbolic Systems of Conservation Laws in One Dimension of Space 55 2.1. Definitions 55 2.1.1. Hyperbolic systems of conservation laws 55 2.1.2. Hyperbolic systems of conservation laws - examples 57 2.1.3. Characteristic form - Riemann invariants 59 2.2. Determination of the solution 62 2.2.1. Domain of influence, domain of dependence 62 2.2.2. Existence and uniqueness of solutions - initial and boundary conditions 64 2.3. Specific case: compressible flows 65 2.3.1. Definition 65 2.3.2. Conservation form 65 2.3.3. Characteristic form 68 2.3.4. Physical inter...
