Mathematical and Computational Methods for Compressible Flow

Erscheinungsjahr 2003
ISBN: 978-0-19-850588-4
Verlag: OUP Oxford

Buch, Englisch, 552 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 986 g

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.

Autoren/Hrsg.

Feistauer, Miloslav

Felcman, Jiri

Straskraba, Ivan

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre

Inhaltsverzeichnis

- 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 for stationary compressible Navier-Stokes equations

- Finite difference and finite volume methods for non-linear hyperbolic systems and the Euler equations

- 3.1: Further properties of the Euler equations

- 3.2: Numerical methods for hyperbolic systems with one space variable

- 3.3: The finite volume method for the multidimensional Euler equations

- 3.4: Osher-Solomon scheme

- 3.5: Higher order finite volume schemes

- 3.6: Adaptive methods

- 3.7: Examples of finite volume simulations

- Finite element solution of compressible flow

- 4.1: Finite element method - elementary treatment

- 4.2: Finite element solution of viscous barotropic flow

- 4.3: Finite element solution of a heat conductive gas flow

- 4.4: Combined finite volume - finite element method for viscous compressible flow

- 4.5: Theory of the combined FV-FE method

- 4.6: Discontinuous Galerkin finite element method

Über Autor(innen)

M. Feistauer is Professor of Mathematics for Approximate and Numerical Methods at Charles University in Prague, Czech Republic. He is a member of the editorial boards for the following journals: Applications of Mathematics, Journal of Numerical Mathematics, Visualization in Science and Computation, Journal of Mathematical Fluid Mechanics and Journal of the Finite Volume Method.

J. Felcman is Associate Professor for Approximate and Numerical Methods at Charles University in Prague, Czech Republic.

I. Straskraba is a research scientist at the Mathematical Institute of the Academy of Sciences in Prague, Czech Republic, and is a member of the editorial board for the Journal of Mathematical Fluid Mechanics.