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 is paid to discontinuous flows, such as steep fronts and shock waves, and their mathematical treatment. Application exercises are given at the end of each chapter, enabling readers to test their understanding of the subject.

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 Buc…