Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 26

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Author: Institute for Computer Applications in Science and Engineering
Publisher:
ISBN:
Category :
Languages : en
Pages : 60

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Author: Heinrich Freistühler
Publisher: Birkhäuser
ISBN: 3034883722
Category : Mathematics
Languages : en
Pages : 471

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Book Description
Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

Author: Alberto Bressan
Publisher: Springer Science & Business Media
ISBN: 1441995544
Category : Mathematics
Languages : en
Pages : 487

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Book Description
This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Author: B. Cockburn
Publisher: Springer
ISBN: 3540498044
Category : Mathematics
Languages : en
Pages : 446

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Book Description
This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Author: Michael Fey
Publisher: Birkhäuser
ISBN: 3034887248
Category : Mathematics
Languages : en
Pages : 514

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Book Description
[Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

Author: Gerald Warnecke
Publisher: Springer Science & Business Media
ISBN: 3540279075
Category : Mathematics
Languages : en
Pages : 541

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Book Description
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.

Author: Thomas Y. Hou
Publisher: Springer Science & Business Media
ISBN: 3642557112
Category : Mathematics
Languages : en
Pages : 946

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Book Description
The International Conference on "Hyperbolic Problems: Theory, Numerics and Applications'' was held in CalTech on March 25-30, 2002. The conference was the ninth meeting in the bi-annual international series which became one of the highest quality and most successful conference series in Applied mathematics. This volume contains more than 90 contributions presented in this conference, including plenary presentations by A. Bressan, P. Degond, R. LeVeque, T.-P. Liu, B. Perthame, C.-W. Shu, B. Sjögreen and S. Ukai. Reflecting the objective of series, the contributions in this volume keep the traditional blend of theory, numerics and applications. The Hyp2002 meeting placed a particular emphasize on fundamental theory and numerical analysis, on multi-scale analysis, modeling and simulations, and on geophysical applications and free boundary problems arising from materials science and multi-component fluid dynamics. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.

Author: Eitan Tadmor
Publisher: American Mathematical Soc.
ISBN: 0821847309
Category : Mathematics
Languages : en
Pages : 690

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Book Description
The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, ``HYP2008'', was held at the University of Maryland from June 9-13, 2008. This was the twelfth meeting in the bi-annual international series of HYP conferences which originated in 1986 at Saint-Etienne, France, and over the last twenty years has become one of the highest quality and most successful conference series in Applied Mathematics. This book, the second in a two-part volume, contains more than sixty articles based on contributed talks given at the conference. The articles are written by leading researchers as well as promising young scientists and cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ``hyperbolic PDEs''. This volume will bring readers to the forefront of research in this most active and important area in applied mathematics.

Author: Andreas Meister
Publisher: Springer Science & Business Media
ISBN: 3322802272
Category : Mathematics
Languages : en
Pages : 329

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Book Description
The book gives an introduction to the fundamental properties of hyperbolic partial differential equations und their appearance in the mathematical modelling of various problems from practice. It shows in an unique manner concepts for the numerical treatment of such equations starting from basic algorithms up actual research topics in this area. The numerical methods discussed are central and upwind schemes for structured and unstructured grids based on ENO and WENO reconstructions, pressure correction schemes like SIMPLE and PISO as well as asymptotic-induced algorithms for low-Mach number flows.