Wave propagation in fluids : models and numerical techniques /
This new edition 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 i...
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| Format: | eBook |
| Language: | English |
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London : Hoboken, NJ :
ISTE ; Wiley,
2010.
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| Edition: | 2nd ed., updated and rev. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Wave Propagation in Fluids; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Scalar Hyperbolic Conservation Laws in One Dimension of Space; 1.1. Definitions; 1.1.1. Hyperbolic scalar conservation laws; 1.1.2. Derivation from general conservation principles; 1.1.3. Non-conservation form; 1.1.4. Characteristic form
- Riemann invariants; 1.2. Determination of the solution; 1.2.1. Representation in the phase space; 1.2.2. Initial conditions, boundary conditions; 1.3. A linear law: the advection equation; 1.3.1. Physical context
- conservation form.
- 1.3.2. Characteristic form1.3.3. Example: movement of a contaminant in a river; 1.3.4. Summary; 1.4. A convex law: the inviscid Burgers equation; 1.4.1. Physical context
- conservation form; 1.4.2. Characteristic form; 1.4.3. Example: propagation of a perturbation in a fluid; 1.4.4. Summary; 1.5. Another convex law: the kinematic wave for free-surface hydraulics; 1.5.1. Physical context
- conservation form; 1.5.2. Non-conservation and characteristic forms; 1.5.3. Expression of the wave speed; 1.5.4. Particular case: flow in a rectangular channel; 1.5.5. Summary.
- 1.6. A non-convex conservation law: the Buckley-Leverett equation1.6.1. Physical context
- conservation form; 1.6.2. Characteristic form; 1.6.3. Example: decontamination of an aquifer; 1.6.4. Summary; 1.7. Advection with adsorption/desorption; 1.7.1. Physical context
- conservation form; 1.7.2. Characteristic form; 1.7.3. Summary; 1.8. Summary of Chapter 1; 1.8.1. What you should remember; 1.8.2. Application exercises; Chapter 2. Hyperbolic Systems of Conservation Laws in One Dimension of Space; 2.1. Definitions; 2.1.1. Hyperbolic systems of conservation laws.
- 2.1.2. Hyperbolic systems of conservation laws
- examples2.1.3. Characteristic form
- Riemann invariants; 2.2. Determination of the solution; 2.2.1. Domain of influence, domain of dependence; 2.2.2. Existence and uniqueness of solutions
- initial and boundary conditions; 2.3. A particular case: compressible flows; 2.3.1. Definition; 2.3.2. Conservation form; 2.3.3. Characteristic form; 2.3.4. Physical interpretation; 2.4. A linear 2×2 system: the water hammer equations; 2.4.1. Physical context
- assumptions; 2.4.2. Conservation form; 2.4.3. Characteristic form
- Riemann invariants.
- 2.4.4. Calculation of the solution2.4.5. Summary; 2.5. A nonlinear 2×2 system: the Saint Venant equations; 2.5.1. Physical context
- assumptions; 2.5.2. Conservation form; 2.5.3. Characteristic form
- Riemann invariants; 2.5.4. Calculation of solutions; 2.5.5. Summary; 2.6. A nonlinear 3×3 system: the Euler equations; 2.6.1. Physical context
- assumptions; 2.6.2. Conservation form; 2.6.3. Characteristic form
- Riemann invariants; 2.6.4. Calculation of the solution; 2.6.5. Summary; 2.7. Summary of Chapter 2; 2.7.1. What you should remember; 2.7.2. Application exercises.