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Analysis and Numerics for Conservation Laws

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Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemi... Weiterlesen
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Beschreibung

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.

Klappentext

The priority research program Analysis and Numerics for Conservation Laws was funded by the German research foundation Deutsche Forschungsgemeinschaft (DFG) for a period of six years starting in 1997. The diversity of topics, represented in the present book, was one of the strengths of the research program. Research groups of very different background, most of which were interacting for the first time, contributed to this interdisciplinary work. The present book contains contributions from interlinked participating projects ranging from the analysis of hyperbolic systems of first order partial differential equations, the development of improved numerical methods for these equations to applications in astrophysics and engineering. It aims at conveying their results achieved in the program to readers outside of their own particular field. The book contains a large number of figures and a number of color plates. The reader can find an up-to-date presentation of many current research topics in the field. TOC:Wave Processes at Interfaces.- Numerics for Magnetoplasmadynamic Propulsion.- Hexagonal Kinetic Models and the Numerical Simulation of Kinetic Boundary Layers.- High-resolution Simulation of Detonations with Detailed Chemistry.- Numerical Linear Stability Analysis for Compressible Fluids.- Simulation of Solar Radiative Magneto-Convection.- Riemann Problem for the Euler Equation with Non-Convex Equation of State Including Phase Transitions.- Radiation Magnetohydrodynamics: Analysis for Model Problems and Efficient 3d-Simulations for the Full System.- Kinetic Schemes for Selected Initial and Boundary Value Problems.- A Local Level-Set Method under Involvement of Topological Aspects.- Hyperbolic Systems and Transport Equations in Mathematical Biology.- Travelling Waves in Systems of Hyperbolic Balance Laws.- The Role of the Jacobian in the Adaptive Discontinuous Galerkin Method for the Compressible Euler Equations.- The Multi-Scale Dust Formation in Substellar Atmospheres.- Meshless Methods for Conservation Laws.- Simulations of Turbulent Thermonuclear Burning in Type Ia Supernovae.- Hyperbolic GLM Scheme for Elliptic Constraints in Computational Electromagnetics and MHD.- Flexible Flame Structure Modelling in a Flame Front Tracking Scheme.- Riemann-Solver Free Schemes.- Relaxation Dynamics, Scaling Limits and Convergence of Relaxation Schemes.- Multidimensional Adaptive Staggered Grids.- On Hyperbolic Relaxation Problems.- Appendix: Color Plates.



Inhalt
S.Andreae, J.Ballmann, S.Müller: Wave Processes at Interfaces.- J.Heiermann, M.Auweter-Kurtz, Ch.Sleziona: Numerics for Magnetoplasmadynamic Propulsion.- H.Babovsky: Hexagonal Kinetic Models and the Numerical Simulation of Kinetic Boundary Layers.- R.Deiterding, G.Bader: High-resolution Simulation of Detonations with Detailed Chemistry.- A.S.Bormann: Numerical Linear Stability Analysis for Compressible Fluids.- M.Schüssler, J.H.M.J.Bruls, A.Vögler, P. Vollmöller: Simulation of Solar Radiative Magneto-Convection.- W.Dahmen, S.Müller, A.Voß: Riemann Problem for the Euler Equation with Non-Convex Equation of State Including Phase Transitions.- A.Dedner, D.Kröner, C.Rohde, M.Wesenberg: Radiation Magnetohydrodynamics: Analysis for Model Problems and Efficient 3d-Simulations for the Full System.- W.Dreyer, M.Herrmann, M.Kunik, S.Qamar: Kinetic Schemes for Selected Initial and Boundary Value Problems.- F.Völker, R.Vilsmeier, D.Hänel: A Local Level-Set Method under Involvement of Topological Aspects.- T.Hillen, K.P.Hadeler: Hyperbolic Systems and Transport Equations in Mathematical Biology.- J.Harterich, St. Liebscher: Travelling Waves in Systems of Hyperbolic Balance Laws.- R.Hartmann: The Role of the Jacobian in the Adaptive Discontinuous Galerkin Method for the Compressible Euler Equations.- Ch.Helling, R.Klein, E.Sedlmayr: The Multi-Scale Dust Formation in Substellar Atmospheres.- D.Hietel, M.Junk, J. Kuhnert, S.Tiwari: Meshless Methods for Conservation Laws.- W.Hillbrandt, M.Reinecke, W.Schmidt, F.K.Röpke, C.Travaglio, J.C.Niemeyer: Simulations of Turbulent Thermonuclear Burining in Type 1a Supernovae.- Y.L.Lee, R.Schneider, C.-D.Munz, F.Kemm: Hyperbolic GLM Scheme for Elliptic Constraints in Computational Electromagnetics and MHD.- H.Schmidt, R.Klein: Flexible Flame Structure Modelling in a Flame Front Tracking Scheme.- T.Kröger, S.Noelle: Riemann-Solver Free Schemes.- H.Liu: Relaxation Dynamics, Scaling Limits and Convergence of Relaxation Schemes.-S.Noelle, W.Rosenbaum, M.Rumpf: Multidimensional Adaptive Staggered Grids.- W.-A.Yong, W.Jäger: On Hyperbolic Relaxation Problems.- Appendix: Color Plates.

Produktinformationen

Titel: Analysis and Numerics for Conservation Laws
EAN: 9783540279075
ISBN: 978-3-540-27907-5
Digitaler Kopierschutz: Wasserzeichen
Format: E-Book (pdf)
Herausgeber: Springer
Genre: Grundlagen
Anzahl Seiten: 542
Veröffentlichung: 05.12.2005
Jahr: 2005
Untertitel: Englisch
Dateigrösse: 30.4 MB