Handbook of Numerical Methods for Hyperbolic Problems - 1st Edition - ISBN: 9780444639103, 9780444639110

Handbook of Numerical Methods for Hyperbolic Problems, Volume 18

1st Edition

Applied and Modern Issues

Editors: Remi Abgrall Chi-Wang Shu
Series Editors: Roland Glowinski Qiang Du Michael Hintermüller Endre Suli
eBook ISBN: 9780444639110
Hardcover ISBN: 9780444639103
Imprint: North Holland
Published Date: 18th January 2017
Page Count: 610
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Table of Contents

  • 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

Description

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.

Key Features

  • 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

Readership

Researchers, graduate students and engineers working on the design, analysis and applications of numerical algorithms for solving hyperbolic partial differential equations


Details

No. of pages:
610
Copyright:
© North Holland 2017
Published:
Imprint:
North Holland
eBook ISBN:
9780444639110
Hardcover ISBN:
9780444639103

About the Editors

Remi Abgrall Editor

Rémi Abgrall is a professor at Universität Zürich

Affiliations and Expertise

Universitat Zurich, Switzerland

Chi-Wang Shu Editor

Professor Chi-Wang Shu is a professor at Brown University, RI, USA

Affiliations and Expertise

Brown University, RI, USA

About the Series Editors

Roland Glowinski Series Editor

Qiang Du Series Editor

Michael Hintermüller Series Editor

Endre Suli Series Editor