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Handbook of Numerical Methods for Hyperbolic Problems
Basic and Fundamental Issues
1st Edition, Volume 17 - November 17, 2016
Editors: Remi Abgrall, Qiang Du, Roland Glowinski, Chi-Wang Shu, Michael Hintermüller, Endre Süli
Language: English
Hardback ISBN:9780444637895
9 7 8 - 0 - 4 4 4 - 6 3 7 8 9 - 5
eBook ISBN:9780444637956
9 7 8 - 0 - 4 4 4 - 6 3 7 9 5 - 6
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and applicati…Read more
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Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations.
This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.
Provides detailed, cutting-edge background explanations of existing algorithms and their analysis
Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis
Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications
Written by leading subject experts in each field who provide breadth and depth of content coverage
Researchers, graduate students and engineers working on the design, analysis and applications of numerical algorithms for solving hyperbolic partial differential equations
Introduction
Acknowledgements
Chapter 1: Introduction to the Theory of Hyperbolic Conservation Laws
Abstract
1 Introduction
2 Basic Structure of Hyperbolic Conservation Laws
3 Strictly Hyperbolic Systems in One Spatial Dimension
Chapter 2: The Riemann Problem: Solvers and Numerical Fluxes
Abstract
1 Preliminaries
2 Exact Solution of the Riemann Problem for the Euler Equations
3 The Roe Approximate Riemann Solver
4 The HLL Approximate Riemann Solver
5 The HLLC Approximate Riemann Solver
6 A Numerical Version of the Osher–Solomon Riemann Solver
7 Other Approaches to Constructing Numerical Fluxes
8 Concluding Remarks
Acknowledgements
Chapter 3: Classical Finite Volume Methods
Abstract
1 Some Philosophical Remarks
2 On the Lax–Wendroff Theorem
3 Historical Remarks
4 Weak Solutions and Finite Volume Methods
5 The Cell-Centred Scheme of Jameson, Schmidt and Turkel
6 Cell-Vertex Schemes on Quadrilateral Grids
7 Finite Volume Methods on Unstructured Grids
Chapter 4: Sharpening Methods for Finite Volume Schemes
Abstract
1 Introduction
2 Sharpening Methods for Linear Equations
3 Coupling With Hyperbolic Nonlinear Equations
Chapter 5: ENO and WENO Schemes
Abstract
1 Introduction
2 ENO and WENO Approximations
3 ENO and WENO Schemes for Hyperbolic Conservation Laws
4 Selected Topics of Recent Developments
Acknowledgements
Chapter 6: Stability Properties of the ENO Method
Abstract
1 Introduction
2 The ENO Reconstruction Method
3 Application to Conservation Laws
4 ENO Stability Properties
5 Summary
Acknowledgements
Chapter 7: Stability, Error Estimate and Limiters of Discontinuous Galerkin Methods
Abstract
1 Introduction
2 Implementation of DG Methods
3 Stability
4 Error Estimates
5 Limiters for Discontinuous Galerkin Methods
6 Concluding and Remarks
Chapter 8: HDG Methods for Hyperbolic Problems
Abstract
1 Introduction
2 The Acoustics Wave Equation
3 The Elastic Wave Equations
4 The Electromagnetic Wave Equations
5 Bibliographic Notes
Acknowledgements
Chapter 9: Spectral Volume and Spectral Difference Methods