Hyperbolic Partial Differential Equations

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

• 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.