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Handbook of Numerical Methods for Hyperbolic Problems
Applied and Modern Issues
1st Edition, Volume 18 - January 16, 2017
Editors: Remi Abgrall, Roland Glowinski, Qiang Du, Chi-Wang Shu, Michael Hintermüller, Endre Süli
Language: English
Hardback ISBN:9780444639103
9 7 8 - 0 - 4 4 4 - 6 3 9 1 0 - 3
eBook ISBN:9780444639110
9 7 8 - 0 - 4 4 4 - 6 3 9 1 1 - 0
Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various n…Read more
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Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. 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 become familiar with their relative advantages and limitations.
Provides detailed, cutting-edge background explanations of existing algorithms and their analysis
Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications
Written by leading subject experts in each field, the volumes 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
Editors’ Introduction
Acknowledgements
Chapter 1: Cut Cells: Meshes and Solvers
Abstract
1 Introduction
2 Brief Early History
3 Mesh Generation
4 Data Structures and Implementation Issues
5 Finite Volume Methods for Cut Cells
6 Conclusions
Acknowledgements
Chapter 2: Inverse Lax–Wendroff Procedure for Numerical Boundary Treatment of Hyperbolic Equations
Abstract
1 Introduction
2 Problem Description and Interior Schemes
3 Numerical Boundary Conditions for Static Geometry
4 Moving Boundary Treatment for Compressible Inviscid Flows
5 Numerical Results
6 Conclusions and Future Work
Chapter 3: Multidimensional Upwinding
Abstract
1 Introduction
2 Why Multidimensional Methods?
3 Oblique Wave Methods
4 “Corner Transport” Methods
5 Edges or Corners?
6 When “Upwinding” Is Not Needed
7 Bicharacteristic Methods
8 Residual Distribution
9 The Poisson Formulas
10 Concluding Remarks
Chapter 4: Bound-Preserving High-Order Schemes
Abstract
1 Introduction
2 A Bound-Preserving Limiter for Approximation Polynomials
3 Bound-Preserving Flux Limiters
4 Concluding Remarks
Acknowledgements
Chapter 5: Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations
Abstract
1 Introduction
2 Basic Design Principles of AP Schemes—Two Illustrative Examples
3 AP Schemes for General Hyperbolic and Kinetic Equations
4 Other Asymptotic Limits and AP Schemes
5 Conclusion
Acknowledgements
Chapter 6: Well-Balanced Schemes and Path-Conservative Numerical Methods
Abstract
1 Introduction
2 Path-Conservative Numerical Schemes
3 Some Families of Path-Conservative Numerical Schemes
4 High-Order Schemes Based on Reconstruction of States
5 Well-Balanced Schemes
6 Convergence and Choice of Paths
Acknowledgements
Chapter 7: A Practical Guide to Deterministic Particle Methods
Abstract
1 Introduction
2 Description of the Particle Method
3 Remeshing for Particle Distortion
4 Applications to Convection–Diffusion Equations
Acknowledgements
Chapter 8: On the Behaviour of Upwind Schemes in the Low Mach Number Limit: A Review
Abstract
1 Introduction
2 The Multiple Low Mach Number Limits of the Compressible Euler Equations
3 Numerical Illustrations
4 Conclusion
Chapter 9: Adjoint Error Estimation and Adaptivity for Hyperbolic Problems
Abstract
1 Introduction
2 Error Representation for Linear Problems
3 A Posteriori Error Estimation
4 Nonlinear Hyperbolic Conservation Laws
5 Practical Implementation and Adaptive Mesh Refinement
6 Applications
7 Concluding Remarks and Outlook
Acknowledgements
Chapter 10: Unstructured Mesh Generation and Adaptation
Abstract
1 Introduction
2 An Introduction to Unstructured Mesh Generation
3 Metric-Based Mesh Adaptation
4 Algorithms for Generating Anisotropic Meshes
5 Adaptive Algorithm and Numerical Illustrations
6 Conclusion
Chapter 11: The Design of Steady State Schemes for Computational Aerodynamics
Abstract
1 Introduction
2 Equations of Gas Dynamics and Spatial Discretizations
3 Time-Marching Methods
4 Newton–Krylov Methods
5 Conclusions
Chapter 12: Some Failures of Riemann Solvers
Abstract
1 Introduction
2 Real Gas Effects
3 Multidimensional Effects
4 Accuracy Effects
Chapter 13: Numerical Methods for the Nonlinear Shallow Water Equations
Abstract
1 Overview
2 Mathematical Model
3 Numerical Methods
4 Shallow Water-Related Models
5 Conclusion Remarks
Acknowledgements
Chapter 14: Maxwell and Magnetohydrodynamic Equations
Abstract
1 Introduction
2 Maxwell's Equations
3 Magnetohydrodynamics
4 Conclusion
Chapter 15: Deterministic Solvers for Nonlinear Collisional Kinetic Flows: A Conservative Spectral Scheme for Boltzmann Type Flows
Abstract
1 Introduction
2 The Landau and Boltzmann Operators Relation Through Their Double Mixing Convolutional Forms
3 A Conservative Spectral Method for the Collisional Form
4 Local Existence, Convergence and Regularity for the Semidiscrete Scheme
5 Final Comments and Conclusions
Acknowledgements
Chapter 16: Numerical Methods for Hyperbolic Nets and Networks
Abstract
1 Introduction
2 Examples of Nets and Networks
3 Numerics for Nets and Networks
Chapter 17: Numerical Methods for Astrophysics
Abstract
1 Introduction
2 Astrophysical Scales for Astrophysical Phenomena
3 Equations Used in Astrophysical Modelling
4 Numerical Methods
5 High-Performance Computing
6 Astrophysical Codes
7 Conclusion
Acknowledgement
Chapter 18: Numerical Methods for Conservation Laws With Discontinuous Coefficients
Abstract
1 Introduction
2 Motivating Examples
3 A Brief Review of Available Theoretical Results
4 Numerical Schemes
5 Numerical Experiments
6 Summary and Open Problems
Acknowledgement
Chapter 19: Uncertainty Quantification for Hyperbolic Systems of Conservation Laws
Abstract
1 Introduction
2 Random Fields and Random Entropy Solutions
3 sG Method for UQ
4 Stochastic Collocation Methods
5 Monte Carlo and Multilevel Monte Carlo Methods
6 Numerical Experiments
7 Measure-Valued and Statistical Solutions
8 Conclusion and Perspectives
Acknowledgements
Chapter 20: Multiscale Methods for Wave Problems in Heterogeneous Media
Abstract
1 Introduction
2 Numerical Methods for the Wave Equation in Heterogeneous Media Without Scale Separation
3 Numerical Methods for the Wave Equation in Heterogeneous Media With Scale Separation
Acknowledgement
Index
No. of pages: 610
Language: English
Edition: 1
Volume: 18
Published: January 16, 2017
Imprint: North Holland
Hardback ISBN: 9780444639103
eBook ISBN: 9780444639110
RA
Remi Abgrall
Rémi Abgrall is a professor at Universität Zürich
Affiliations and expertise
Universitat Zurich, Switzerland
CS
Chi-Wang Shu
Professor Chi-Wang Shu is a professor at Brown University, RI, USA
Affiliations and expertise
Brown University, RI, USA
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