Hyperbolic Partial Differential Equations
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Hyperbolic Partial Differential Equations: Theory, Numerics and Applications

Hyperbolic Partial Differential Equations: Theory, Numerics and Applications


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About the Book

Neben einer Einführung in die fundamentalen Eigenschaften hyperbolischer Differentialgleichungen und Ihrer Entstehung bei der Modellierung unterschiedlicher praxisrelevanter Problemstellungen stellen die Verfasser in diesem Lehrbuch Konzepte numerischer Methoden und Analysis von den Grundlagen bis zu den neuesten Entwicklungen in einer eingängigen Form vor. Hierbei werden zentrale Verfahren wie auch Upwind-Methoden auf strukturierten und unstrukturierten Gitter basierend auf ENO- und WENO-Rekonstruktionstechniken diskutiert und neben Druckkorrekturverfahren wie bespielsweise SIMPLE und PISO auch asymptotisch-basierte Algorithmen für Strömungen kleiner Mach-Zahl vorgestellt. Die Themen haben praktische Anwendungen in Technik und Physik.

Table of Contents:
1 Hyperbolic Conservation Laws and Industrial Applications.- 1.1 Transport theorem and balance laws.- 1.2 Linear initial and boundary value problems.- 1.3 Weak solutions and entropy.- 1.4 Systems of conservation laws.- 2 Central Schemes and Systems of Balance Laws.- 2.1 Second order central schemes.- 2.2 High order central schemes.- 2.3 Multidimensional central schemes.- 2.4 Treatment of the source.- Further developments.- 3 Methods on unstructured grids, WENO and ENO Recovery techniques.- 3.1 Introduction to finite volume approximations.- 3.2 Governing equations.- 3.3 Finite volume approximations.- 3.4 Time stepping schemes.- 3.5 Remarks on the philosophy of ENO schemes.- 3.6 Polynomial recovery.- 3.7 WENO approximations.- 3.8 The theory of optimal recovery.- 3.9 Grid adaptivity for box methods.- 3.10 Error and residual.- 3.11 Experience with L2.- 3.12 The dual graph-norm.- 3.13 Closing of the circle: L2 meets dual graph norm.- 4 Pressure-Correction Methods for all Flow Speeds.- 4.1 Introduction.- 4.2 Conservation Equations.- 4.3 Pressure-Correction Equation for Incompressible Flows.- 4.4 Pressure-Correction Equation for Compressible Flows.- 4.5 Solution Algorithm for all Flow Speeds.- 4.6 FV-Method for Arbitrary Control Volumes.- 4.7 Pressure-Correction Algorithm for FV-Methods.- 4.8 Implementation of Boundary Conditions.- 4.9 Examples of Application.- 4.10 Conclusions.- 5 Computational Fluid Dynamics and Aeroacoustics for Low Mach Number Flow.- 5.1 Introduction.- 5.2 Non-Dimensionalisation of the Governing Equations.- 5.3 The Incompressible Limit of a Compressible Fluid Flow.- 5.4 Numerical Methods for Low Mach Number Fluid Flow.- 5.5 Sound Generation and Sound Propagation.- 5.6 Multiple Scale Considerations.- 5.7 Numerical Aeroacoustics.- 5.8 Conclusions.

About the Author :
Herausgeber: Prof. Dr. Andreas Meister, FB Mathematik und Informatik, Universität Kassel und Prof. Dr. Jens Struckmeier, Institut für Angewandte Mathematik, Universität Hamburg.


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Product Details
  • ISBN-13: 9783322802293
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 240 mm
  • No of Pages: 320
  • Sub Title: Theory, Numerics and Applications
  • ISBN-10: 3322802299
  • Publisher Date: 30 Dec 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Width: 170 mm


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Hyperbolic Partial Differential Equations: Theory, Numerics and Applications
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