Dr. Rainer Ansorge Em. Professor of Mathematics Technical University Hamburg-Harburg Hamburg, Germany Rainer Ansorge studied Mathematics and Physics at the Free University and Technical University (TU) of Berlin, Germany. After positions as computational engineer at the Volkswagen Company (1956) he became Full Professor of Mathematics at the University of Hamburg, Germany (1969). He was one of the founders of the TU Hamburg-Harburg (1974-1986) and his scientific research activities are covering more than 20 countries. Prof. Ansorge is member of the European Academy of Sciences and Arts, of the New York Academy of Sciences and the GAMM. Prof. Dr. Thomas Sonar University of Braunschweig Institute of Computational Physics Braunschweig, Germany Prof. Sonar is head of the group Partial Differential Equations at the Institute of Computational Mathematics of the University of Braunschweig. His main fields are: Numerics of the partial differential equations, numerical fluid mechanics and analysis of discrete data.

Dr. Rainer Ansorge Em. Professor für Mathematik Technische Universität Hamburg-Harburg Hamburg, Germany Prof. Ansorge ist Autor von drei Büchern und über 70 Artikeln in mehr als 20 renommierten internationalen Zeitschriften und Mitglied im Editorial Board mehrerer internationaler Zeitschriften. Prof. Dr. Thomas Sonar Universität Braunschweig Institut Computational Physics Braunschweig, Germany Prof. Sonar ist Leiter der Arbeitsgruppe Partielle Differentialgleichungen im Institut Computational Mathematics der Universität Braunschweig. Fachgebiete: Numerik partieller Differentialgleichungen, Numerische Strömungsmechanik, Analyse diskreter Daten.

1. Ideal Fluids
2. Weak Solutions of Conservation Laws
3. Entropy Conditions
4. The Riemann Problem
5. Real Fluids
6. Existence Proof for Entropy Solutions by Means of Discretization Procedures
7. Types of Discretization Principles
8. A Closer Look into Discrete Models
9. Discrete Models on Curvilinear Grids
10. Finite Volume Models
11. Simple Meshless Models 1. Ideal Fluids
2. Weak Solutions of Conservation Laws
3. Entropy Conditions
4. The Riemann Problem
5. Real Fluids
6. Existence Proof for Entropy Solutions by Means of Discretization Procedures
7. Types of Discretization Principles
8. A Closer Look into Discrete Models
9. Discrete Models on Curvilinear Grids
10. Finite Volume Models
11. Simple Meshless Models

"The book is useful for students and experts, for mathematicians with interest on physical/technical problems, and for engineers in the field of fluid dynamics."

B. Platzer
ZAMM No. 9, 1 (2004)