## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

## Book Description

Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior and graduate level students, especially in aerospace engineering, as well as researchers and practising engineers, will find a wealth of invaluable information on high-speed gas flows in this text.

1. Cover
2. Half Title
3. Title Page
5. Contents
6. Preface
7. Chapter 1. Introduction
8. Part I: Gasdynamics Review
1. Chapter 2. Governing Equations of Gasdynamics
1. 2.0 Introduction
2. 2.1 The Integral Form of the Euler Equations
3. 2.2 The Conservation Form of the Euler Equations
4. 2.3 The Primitive Variable Form of the Euler Equations
5. 2.4 Other Forms of the Euler Equations
2. Chapter 3. Waves
1. 3.0 Introduction
2. 3.1 Waves for a Scalar Model Problem
3. 3.2 Waves for a Vector Model Problem
4. 3.3 The Characteristic Form of the Euler Equations
5. 3.4 Simple Waves
6. 3.5 Expansion Waves
7. 3.6 Compression Waves and Shock Waves
8. 3.7 Contact Discontinuities
3. Chapter 4. Scalar Conservation Laws
4. Chapter 5. The Riemann Problem
1. 5.0 Introduction
2. 5.1 The Riemann Problem for the Euler Equations
3. 5.2 The Riemann Problem for Linear Systems of Equations
4. 5.3 Three-Wave Linear Approximations – Roe’s Approximate Riemann Solver for the Euler Equations
5. 5.4 One-Wave Linear Approximations
6. 5.5 Other Approximate Riemann Solvers
7. 5.6 The Riemann Problem for Scalar Conservation Laws
9. Part II: Computational Review
1. Chapter 6. Numerical Error
2. Chapter 7. Orthogonal Functions
3. Chapter 8. Interpolation
1. 8.0 Introduction
2. 8.1 Polynomial Interpolation
3. 8.2 Trigonometric Interpolation and the Nyquist Sampling Theorem
4. Chapter 9. Piecewise-Polynomial Reconstruction
5. Chapter 10. Numerical Calculus
1. 10.0 Introduction
2. 10.1 Numerical Differentiation
3. 10.2 Numerical Integration
4. 10.3 Runge–Kutta Methods for Solving Ordinary Differential Equations
10. Part III: Basic Principles of Computational Gasdynamics
1. Chapter 11. Conservation and Other Basic Principles
1. 11.0 Introduction
2. 11.1 Conservative Finite-Volume Methods
3. 11.2 Conservative Finite-Difference Methods
4. 11.3 Transformation to Conservation Form
2. Chapter 12. The CFL Condition
3. Chapter 13. Upwind and Adaptive Stencils
1. 13.0 Introduction
2. 13.1 Scalar Conservation Laws
3. 13.2 The Euler Equations
4. 13.3 Introduction to Flux Averaging
5. 13.4 Introduction to Flux Splitting
6. 13.5 Introduction to Wave Speed Splitting
7. 13.6 Introduction to Reconstruction–Evolution Methods
4. Chapter 14. Artificial Viscosity
5. Chapter 15. Linear Stability
6. Chapter 16. Nonlinear Stability
11. Part IV: Basic Methods of Computational Gasdynamics
1. Chapter 17. Basic Numerical Methods for Scalar Conservation Laws
1. 17.0 Introduction
2. 17.1 Lax–Friedrichs Method
3. 17.2 Lax–Wendroff Method
4. 17.3 First-Order Upwind Methods
5. 17.4 Beam–Warming Second-Order Upwind Method
6. 17.5 Fromm’s Method
2. Chapter 18. Basic Numerical Methods for the Euler Equations
1. 18.0 Introduction
2. 18.1 Flux Approach
3. 18.2 Wave Approach I: Flux Vector Splitting
4. 18.3 Wave Approach II: Reconstruction–Evolution
3. Chapter 19. Boundary Treatments
12. Part V: Advanced Methods of Computational Gasdynamics
1. Chapter 20. Flux Averaging I: Flux-Limited Methods
1. 20.0 Introduction
2. 20.1 Van Leer’s Flux-Limited Method
3. 20.2 Sweby’s Flux-Limited Method (TVD)
4. 20.3 Chakravarthy–Osher Flux-Limited Methods (TVD)
5. 20.4 Davis–Roe Flux-Limited Method (TVD)
6. 20.5 Yee–Roe Flux-Limited Method (TVD)
2. Chapter 21. Flux Averaging II: Flux-Corrected Methods
1. 21.0 Introduction
2. 21.1 Boris–Book Flux-Corrected Method (FCT)
3. 21.2 Zalesak’s Flux-Corrected Methods (FCT)
4. 21.3 Harten’s Flux-Corrected Method (TVD)
5. 21.4 Shu–Osher Methods (ENO)
3. Chapter 22. Flux Averaging III: Self-Adjusting Hybrid Methods
1. 22.0 Introduction
2. 22.1 Harten–Zwas Self-Adjusting Hybrid Method
3. 22.2 Harten’s Self-Adjusting Hybrid Method
4. 22.3 Jameson’s Self-Adjusting Hybrid Method
4. Chapter 23. Solution Averaging: Reconstruction–Evolution Methods
1. 23.0 Introduction
2. 23.1 Van Leer’s Reconstruction–Evolution Method (MUSCL)
3. 23.2 Colella–Woodward Reconstruction–Evolution Method (PPM)
4. 23.3 Anderson–Thomas–Van Leer Reconstruction–Evolution Methods (TVD/MUSCL): Finite-Volume Versions of the Chakravarthy–Osher Flux-Corrected Methods
5. 23.4 Harten–Osher Reconstruction–Evolution Method (UNO)
6. 23.5 Harten–Engquist–Osher–Chakravarthy Reconstruction–Evolution Methods (ENO)
5. Chapter 24. A Brief Introduction to Multidimensions
13. Index