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Finite Volume Methods for Hyperbolic Problems

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Finite Volume Methods for Hyperbolic Problems
Randall J. Leveque

Table of Contents

1 Introduction

Part 1 Linear Equations

2 Conservation Laws and Differential Equations

3 Characteristics and Riemann Problems for Linear Hyperbolic Equations

4 Finite Volume Methods

5 Introduction to the CLAWPACK Software

6 High-Resolution Methods

7 Boundary Conditions and Ghost Cells

8 Convergence, Accuracy, and Stability

9 Variable-Coefficient Linear Equations

10 Other Approaches to High Resolution

Part II Nonlinear Equations

11 Nonlinear Scalar Conservation Laws

12 Finite Volume Methods for Nonlinear Scalar Conservation Laws

13 Nonlinear Systems of Conservation Laws

14 Gas Dynamics and the Euler Equations

15 Finite Volume Methods for Nonlinear Systems

16 Some Nonclassical Hyperbolic Problems

17 Source Terms and Balance Laws

Part III Multidimensional Problems

18 Multidimensional Hyperbolic Problems

19 Multidimensional Numerical Methods

20 Multidimensional Scalar Equations

21 Multidimensional Systems

22 Elastic Waves

23 Finite Volume Methods on Quadrilateral Grids

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