"Wave Propagation in Fluids: Models and Numerical Techniques" by Vincent Guinot

This edition 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.


Contents
Introduction
1 Scalar Hyperbolic Conservation Laws in One Dimension of Space
2 Hyperbolic Systems of Conservation Laws in One Dimension of Space
3 Weak Solutions and their Properties
4 The Riemann Problem
5 Multidimensional Hyperbolic Systems
6 Finite Difference Methods for Hyperbolic Systems
7 Finite Volume Methods for Hyperbolic Systems
8 Finite Element Methods fo rHyperbolic Systems
9 Treatment of Source Terms
10 Sensitivity Equations for Hyperbolic Systems
11 Modeling in Practice
Appendix A: Linear Algebra
Appendix B: Numerical Analysis
Appendix C: Approximate Riemann Solvers
Appendix D: Summary of the Formulae
Bibliography
Index