Analysis and Numerics for Conservation Laws

1. Front Matter

   Pages I-X

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2. Wave Processes at Interfaces

   • Sigrid Andreae, Josef Ballmann, Siegfried Müller

   Pages 1-25

3. Numerics for Magnetoplasmadynamic Propulsion

   • Jörg Heiermann, Monika Auweter-Kurtz, Christian Sleziona

   Pages 27-45

4. Hexagonal Kinetic Models and the Numerical Simulation of Kinetic Boundary Layers

   • Hans Babovsky

   Pages 47-67

5. High-resolution Simulation of Detonations with Detailed Chemistry

   • Ralf Deiterding, Georg Bader

   Pages 69-91

6. Numerical Linear Stability Analysis for Compressible Fluids

   • Andreas S. Bormann

   Pages 93-105

7. Simulation of Solar Radiative Magneto-Convection

   • M. Schüssler, J.H.M.J. Bruls, A. Vögler, P. Vollmöller

   Pages 107-136

8. Riemann Problem for the Euler Equation with Non-Convex Equation of State including Phase Transitions

   • Wolfgang Dahmen, Siegfried Müller, Alexander Voß

   Pages 137-162

9. Radiation Magnetohydrodynamics: Analysis for Model Problems and Efficient 3d-Simulations for the Full System

   • A. Dedner, D. Kröner, C. Rohde, M. Wesenberg

   Pages 163-202

10. Kinetic Schemes for Selected Initial and Boundary Value Problems

    • Wolfgang Dreyer, Michael Herrmann, Matthias Kunik, Shamsul Qamar

    Pages 203-232

11. A Local Level-Set Method under Involvement of Topological Aspects

    • F. Völker, R. Vilsmeier, D. Hänel

    Pages 233-256

12. Hyperbolic Systems and Transport Equations in Mathematical Biology

    • T. Hillen, K.P. Hadeler

    Pages 257-279

13. Travelling Waves in Systems of Hyperbolic Balance Laws

    • Jörg Härterich, Stefan Liebscher

    Pages 281-300

14. The Role of the Jacobian in the Adaptive Discontinuous Galerkin Method for the Compressible Euler Equations

    • Ralf Hartmann

    Pages 301-316

15. The Multi-Scale Dust Formation in Substellar Atmospheres

    • Christiane Helling, Rupert Klein, Erwin Sedlmayr

    Pages 317-337

16. Meshless Methods for Conservation Laws

    • D. Hietel, M. Junk, J. Kuhnert, S. Tiwari

    Pages 339-362

17. Simulations of Turbulent Thermonuclear Burning in Type Ia Supernovae

    • W. Hillebrandt, M. Reinecke, W. Schmidt, F.K. Röpke, C. Travaglio, J.C. Niemeyer

    Pages 363-384

18. Hyperbolic GLM Scheme for Elliptic Constraints in Computational Electromagnetics and MHD

    • Y.J. Lee, R. Schneider, C.-D. Munz, F. Kemm

    Pages 385-404

19. Flexible Flame Structure Modelling in a Flame Front Tracking Scheme

    • Heiko Schmidt, Rupert Klein

    Pages 405-427

20. Riemann-Solver Free Schemes

    • Tim Kröger, Sebastian Noelle

    Pages 429-451

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.

• 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

• Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

  Gerald Warnecke

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