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Hyperbolic Partial Differential Equations Theory, Numerics and Applications

The book gives an introduction to the fundamental properties of hyperbolic partial differential equations und their appearance in the mathematical modeling of various problems from practice. It shows in an unique manner concepts for the numerical treatment of such equations starting from basic algor...

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Bibliographic Details
Other Authors: Meister, Andreas (Editor), Struckmeier, Jens (Editor)
Format: eBook
Language:English
Published: Wiesbaden Vieweg+Teubner Verlag 2002, 2002
Edition:1st ed. 2002
Subjects:
Mathematical Analysis
Analysis
Differential Equations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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

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