Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues

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 analysisIdeal for readers working on the theoretical aspects of algorithm development and its numerical analysisPresents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applicationsWritten by leading subject experts in each field who provide breadth and depth of content coverage

General Introduction

R. Abgrall and C.-W. Shu

Introduction to the Theory of Hyperbolic Conservation Laws

C.M. Dafermos

The Riemann Problem: Solvers and Numerical Fluxes

E.F. Toro

Classical Finite Volume Methods

T. Sonar

Sharpening Methods for Finite Volume Schemes

B. Després, S. Kokh and F. Lagoutière

ENO and WENO Schemes

Y.-T. Zhang and C.-W. Shu

Stability Properties of the ENO Method

U.S. Fjordholm

Stability, Error Estimate and Limiters of Discontinuous Galerkin Methods

J. Qiu and Q. Zhang

HDG Methods for Hyperbolic Problems

B. Cockburn, N.C. Nguyen and J. Peraire

Spectral Volume and Spectral Difference Methods

Z.J. Wang, Y. Liu, C. Lacor and J. Azevedo

High-Order Flux Reconstruction Schemes

F.D. Witherden, P.E. Vincent and A. Jameson

Linear Stabilization for First-Order PDEs

A. Ern and J.-L. Guermond

Least-Squares Methods for Hyperbolic Problems

P. Bochev and M. Gunzburger

Staggered and Co-Located Finite Volume Schemes for Lagrangian

Hydrodynamics

R. Loubère, P.-H. Maire and B. Rebourcet

High Order Mass Conservative Semi-Lagrangian Methods for Transport Problems

J.-M. Qiu

Front Tracking Methods

D. She, R. Kaufman, H. Lim, J. Melvin, A. Hsu and J. Glimm

Moretti’s Shock-Fitting Methods on Structured and Unstructured Meshes

A. Bonfiglioli, R. Paciorri, F. Nasuti and M. Onofri

Spectral Methods for Hyperbolic Problems

J.S. Hesthaven

Entropy Stable Schemes

E. Tadmor

Entropy Stable Summation-By-Parts Formulations for Compressible Computational Fluid Dynamics

M.H. Carpenter, T.C. Fisher, E.J. Nielsen, M. Parsani, M. Svärd and N. Yamaleev

Central Schemes: A Powerful Black-Box Solver for Nonlinear Hyperbolic PDEs

A. Kurganov

Time Discretization Techniques

S. Gottlieb and D.I. Ketcheson

The Fast Sweeping Method for Stationary Hamilton-Jacobi Equations

H. Zhao

Numerical Methods for Hamilton˗Jacobi Type Equations

M. Falcone and R. Ferretti