High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This text book gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows. Fachgebiet: Numerical Methods Zielgruppe: Research and Development

In 1917, the British scientist L. F. Richardson made the first reported attempt to predict the weather by solving partial differential equations numerically, by hand! It is generally accepted that Richardson's work, though unsuccess­ ful, marked the beginning of Computational Fluid Dynamics (CFD), a large branch of Scientific Computing today. His work had the four distinguishing characteristics of CFD: a PRACTICAL PROBLEM to solve, a MATHEMATICAL MODEL to represent the problem in the form of a set of partial differen­ tial equations, a NUMERICAL METHOD and a COMPUTER, human beings in Richardson's case. Eighty years on and these four elements remain the pillars of modern CFD. It is therefore not surprising that the generally accepted definition of CFD as the science of computing numerical solutions to Partial Differential or Integral Equations that are models for fluid flow phenomena, closely embodies Richardson's work. COMPUTERS have, since Richardson's era, developed to unprecedented levels and at an ever decreasing cost. PRACTICAL PROBLEMS to solved nu­ merically have increased dramatically. In addition to the traditional demands from Meteorology, Oceanography, some branches of Physics and from a range of Engineering Disciplines, there are at present fresh demands from a dynamic and fast-moving manufacturing industry, whose traditional build-test-fix approach is rapidly being replaced by the use of quantitative methods, at all levels. The need for new materials and for decision-making under envi­ ronmental constraints are increasing sources of demands for mathematical modelling, numerical algorithms and high-performance computing.

1. The Equations of Fluid Dynamics.- 2. Notions on Hyperbolic Partial Differential Equations.- 3. Some Properties of the Euler Equations.- 4. The Riemann Problem for the Euler Equations.- 5. Notions on Numerical Methods.- 6. The Method of Godunov for Non-linear Systems.- 7. Random Choice and Related Methods.- 8. Flux Vector Splitting Methods.- 9. Approximate-State Riemann Solvers.- 10. The HLL and HLLC Riemann Solvers.- 11. The Riemann Solver of Roe.- 12. The Riemann Solver of Osher.- 13. High-Order and TVD Methods for Scalar Problems.- 14. High-Order and TVD Schemes for Non-Linear Systems.- 15. Splitting Schemes for PDEs with Source Terms.- 16. Methods for Multi-Dimensional PDEs.- 17. Multidimensional Test Problems.- 18. Concluding Remarks.