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Book Information
Title*

"Numerical Approximation of Hyperbolic Systems of Conservation Laws"
Subtitle (any additional title information)

"Applied Mathematical Sciences, Vol 118"
Authors* (last, first; last, first)

"Godlewski, Edwige; Raviart, Pierre-Arnaud"
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Book Description
Book Categories* (mark the most apporpriate categories that the book belongs in)

"Numerical Methods"

Brief Description*
(a summary of the subjects covered in the book)

"This book covers the theory and approximation of nonlinear hyperbolic systems of conservation laws in one or two spaces variables."

Keywords
(separate with commas)

"numerical method, algorithm, hyperbolic, nonlinear, reacting, multidimensional"

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Table of Contents


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  Preface  
  Introduction 1
1 Definitions and examples  
2 Weak solutions of systems of conservation laws  
3 Entropy solutions  
  Notes  
     
I Nonlinear hyperbolic systems in one space dimension 37
1 Linear hyperbolic systems with constant coefficients  
2 The nonlinear case. Definitions and examples  
3 Simple waves and Riemann invariants  
4 Shock waves and contact discontinuties  
5 Characteristic curves and entropy conditions  
6 Solution of the Riemann problem  
7 The Riemann problem for the p-system  
  Notes  
     
II Gas dynamics and reacting flows 99
1 Preliminaries  
2 Entropy satisfying shock conditions  
3 Solution of the Riemann problem  
4 Reacting flows. The Chapman-Jouguet theory  
5 Reacting flows. The Z. N. D. model for detonations  
  Notes  
     
III Finite difference schemes for one-dimensional systems 167
1 Generalities on finite difference methods for systems  
2 Godunov's method  
3 Roe's method  
4 The Osher scheme  
5 Flux vector splitting methods  
6 Van Leer's second-order method  
7 Kinetic schemes for the Euler equations  
  Notes  
     
IV The case of multidimensional systems 303
1 Generalities on multidimensional hyperbolic systems  
2 The gas dynamics equations in two space dimensions  
3 Multidimensional finite difference schemes  
4 Finite-volume methods  
5 Second-order finite-volume schemes  
  Notes  
     
V An introduction to boundary conditions. 417
1 The initial boundary value problem in the linear case  
2 The nonlinear approach  
3 Gas dynamics  
4 Absorbing boundary conditions  
5 Numerical treatment  
  Notes  
     
  Bibliography 461
  Index 501

  Preface  
  Introduction 1
1 Definitions and examples  
2 Weak solutions of systems of conservation laws  
3 Entropy solutions  
  Notes  
     
I Nonlinear hyperbolic systems in one space dimension 37
1 Linear hyperbolic systems with constant coefficients  
2 The nonlinear case. Definitions and examples  
3 Simple waves and Riemann invariants  
4 Shock waves and contact discontinuties  
5 Characteristic curves and entropy conditions  
6 Solution of the Riemann problem  
7 The Riemann problem for the p-system  
  Notes  
     
II Gas dynamics and reacting flows 99
1 Preliminaries  
2 Entropy satisfying shock conditions  
3 Solution of the Riemann problem  
4 Reacting flows. The Chapman-Jouguet theory  
5 Reacting flows. The Z. N. D. model for detonations  
  Notes  
     
III Finite difference schemes for one-dimensional systems 167
1 Generalities on finite difference methods for systems  
2 Godunov's method  
3 Roe's method  
4 The Osher scheme  
5 Flux vector splitting methods  
6 Van Leer's second-order method  
7 Kinetic schemes for the Euler equations  
  Notes  
     
IV The case of multidimensional systems 303
1 Generalities on multidimensional hyperbolic systems  
2 The gas dynamics equations in two space dimensions  
3 Multidimensional finite difference schemes  
4 Finite-volume methods  
5 Second-order finite-volume schemes  
  Notes  
     
V An introduction to boundary conditions. 417
1 The initial boundary value problem in the linear case  
2 The nonlinear approach  
3 Gas dynamics  
4 Absorbing boundary conditions  
5 Numerical treatment  
  Notes  
     
  Bibliography 461
  Index 501

 
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