Mathematical and Computational Methods for Compressible Flow [Hardcover]

This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow.

Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems.

The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.




Fundamental concepts and equations
1.1. Some mathematical concepts and notation
1.2. Governing equations and relations of gas dynamics
1.3. Some advanced mathematical concepts and results
1.4. Survey of concepts and results from functional analysis
Basic facts from the theory of the Euler and Navier-Stokes equations
2.1. Hyperbolic systems and the Euler equations
2.2. Existence of smooth solutions
2.3. Weak solutions
2.4. Nonstationary Navier-Stokes equations of compressible flow
2.5. Existence results lsJ