Analysis and Numerics for Conservation Laws

  • Gerald Warnecke

Table of contents

  1. Front Matter
    Pages I-X
  2. Sigrid Andreae, Josef Ballmann, Siegfried Müller
    Pages 1-25
  3. Jörg Heiermann, Monika Auweter-Kurtz, Christian Sleziona
    Pages 27-45
  4. M. Schüssler, J.H.M.J. Bruls, A. Vögler, P. Vollmöller
    Pages 107-136
  5. Wolfgang Dahmen, Siegfried Müller, Alexander Voß
    Pages 137-162
  6. Wolfgang Dreyer, Michael Herrmann, Matthias Kunik, Shamsul Qamar
    Pages 203-232
  7. F. Völker, R. Vilsmeier, D. Hänel
    Pages 233-256
  8. Jörg Härterich, Stefan Liebscher
    Pages 281-300
  9. Christiane Helling, Rupert Klein, Erwin Sedlmayr
    Pages 317-337
  10. D. Hietel, M. Junk, J. Kuhnert, S. Tiwari
    Pages 339-362
  11. W. Hillebrandt, M. Reinecke, W. Schmidt, F.K. Röpke, C. Travaglio, J.C. Niemeyer
    Pages 363-384
  12. Y.J. Lee, R. Schneider, C.-D. Munz, F. Kemm
    Pages 385-404
  13. Tim Kröger, Sebastian Noelle
    Pages 429-451

About this book

Introduction

Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics.

Keywords

astrophysics calculus computational astrophysics computational fluid dynamics convection differential equation dynamics fluid dynamics hyperbolic conservation laws magnetohydrodynamics numerical methods numerics partial differential equation stability waves

Editors and affiliations

  • Gerald Warnecke
    • 1
  1. 1.Institut für Analysis und NumerikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-27907-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-24834-7
  • Online ISBN 978-3-540-27907-5
  • About this book