Author | Meister, Andreas. author |
---|---|

Title | Hyperbolic Partial Differential Equations [electronic resource] : Theory, Numerics and Applications / by Andreas Meister, Jens Struckmeier |

Imprint | Wiesbaden : Vieweg+Teubner Verlag, 2002 |

Connect to | http://dx.doi.org/10.1007/978-3-322-80227-9 |

Descript | XII, 320 p. online resource |

SUMMARY

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 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. The book is mainly written for students from mathematics, physics and engineering but also well suited for researchers from academic institutes and industry

CONTENT

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

Mathematics
Mathematical analysis
Analysis (Mathematics)
Partial differential equations
Mathematics
Partial Differential Equations
Analysis