You are previewing Computational Aeroacoustics.
O'Reilly logo
Computational Aeroacoustics

Book Description

Computational aeroacoustics (CAA) is a relatively new research area. CAA algorithms have developed rapidly and the methods have been applied in many areas of aeroacoustics. The objective of CAA is not simply to develop computational methods but also to use these methods to solve practical aeroacoustics problems and to perform numerical simulation of aeroacoustic phenomena. By analysing the simulation data, an investigator can determine noise generation mechanisms and sound propagation processes. This is both a textbook for graduate students and a reference for researchers in CAA and as such is self-contained. No prior knowledge of numerical methods for solving partial differential equations (PDEs) is needed, however, a general understanding of partial differential equations and basic numerical analysis is assumed. Exercises are included and are designed to be an integral part of the chapter content. In addition, sample computer programs are included to illustrate the implementation of the numerical algorithms.

Table of Contents

  1. Coverpage
  2. Computational Aeroacoustics
  3. Title page
  4. Copyright page
  5. Contents
  6. Preface
  7. 1. Finite Difference Equations
    1. 1.1 Order of Finite Difference Equations: Concept of Solution
    2. 1.2 Linear Difference Equations with Constant Coefficients
    3. 1.3 Finite Difference Solution as an Approximate Solution of a Boundary Value Problem
    4. 1.4 Finite Difference Model for a Surface of Discontinuity
    5. Exercises
  8. 2. Spatial Discretization in Wave Number Space
    1. 2.1 Truncated Taylor Series Method
    2. 2.2 Optimized Finite Difference Approximation in Wave Number Space
    3. 2.3 Group Velocity Consideration
    4. 2.4 Schemes with Large Stencils
    5. 2.5 Backward Difference Stencils
    6. 2.6 Coefficients of Several Large Optimized Stencils
    7. Exercises
  9. 3. Time Discretization
    1. 3.1 Single Time Step Method: Runge-Kutta Scheme
    2. 3.2 Optimized Multilevel Time Discretization
    3. 3.3 Stability Diagram
    4. Exercises
  10. 4. Finite Difference Scheme as Dispersive Waves
    1. 4.1 Dispersive Waves of Physical Systems
    2. 4.2 Group Velocity and Dispersion
    3. 4.3 Origin of Numerical Dispersion
    4. 4.4 Numerical Dispersion Arising from Temporal Discretization
    5. 4.5 Origin of Numerical Dissipation
    6. 4.6 Multidimensional Waves
    7. Exercises
  11. 5. Finite Difference Solution of the Linearized Euler Equations
    1. 5.1 Dispersion Relations and Asymptotic Solutions of the Linearized Euler Equations
    2. 5.2 Dispersion-Relation-Preserving (DRP) Scheme
    3. 5.3 Numerical Stability
    4. 5.4 Group Velocity for Finite Difference Schemes
    5. 5.5 Time Step Δt: Accuracy Consideration
    6. 5.6 DRP Scheme in Curvilinear Coordinates
    7. Exercises
  12. 6. Radiation, Outflow, and Wall Boundary Conditions
    1. 6.1 Radiation Boundary Conditions
    2. 6.2 Outflow Boundary Conditions
    3. 6.3 Implementation of Radiation and Outflow Boundary Conditions
    4. 6.4 Numerical Simulation: An Example
    5. 6.5 Generalized Radiation and Outflow Boundary Conditions
    6. 6.6 The Ghost Point Method for Wall Boundary Conditions
    7. 6.7 Enforcing Wall Boundary Conditions on Curved Surfaces
    8. Exercises
  13. 7. The Short Wave Component of Finite Difference Schemes
    1. 7.1 The Short Waves
    2. 7.2 Artificial Selective Damping
    3. 7.3 Excessive Damping
    4. 7.4 Artificial Damping at Surfaces of Discontinuity
    5. 7.5 Aliasing
    6. 7.6 Coefficients of Several Large Damping Stencils
    7. Exercises
  14. 8. Computation of Nonlinear Acoustic Waves
    1. 8.1 Nonlinear Simple Waves
    2. 8.2 Spurious Oscillations: Origin and Characteristics
    3. 8.3 Variable Artificial Selective Damping
    4. Exercises
  15. 9. Advanced Numerical Boundary Treatments
    1. 9.1 Boundaries with Incoming Disturbances
    2. 9.2 Entrainment Flow
    3. 9.3 Outflow Boundary Conditions: Further Consideration
    4. 9.4 Axis Boundary Treatment
    5. 9.5 Perfectly Matched Layer as an Absorbing Boundary Condition
    6. 9.6 Boundaries with Discontinuities
    7. 9.7 Internal Flow Driven by a Pressure Gradient
    8. Exercises
  16. 10. Time-Domain Impedance Boundary Condition
    1. 10.1 A Three-Parameter Broadband Model
    2. 10.2 Stability of the Three-Parameter Time-Domain Impedance Boundary Condition
    3. 10.3 Impedance Boundary Condition in the Presence of a Subsonic Mean Flow
    4. 10.4 Numerical Implementation
    5. 10.5 A Numerical Example
    6. 10.6 Acoustic Wave Propagation and Scattering in a Duct with Acoustic Liner Splices
    7. Exercises
  17. 11. Extrapolation and Interpolation
    1. 11.1 Extrapolation and Numerical Instability
    2. 11.2 Wave Number Analysis of Extrapolation
    3. 11.3 Optimized Interpolation Method
    4. 11.4 A Numerical Example
    5. Exercises
  18. 12. Multiscales Problems
    1. 12.1 Spatial Stencils for Use in the Mesh-Size-Change Buffer Region
    2. 12.2 Time Marching Stencil
    3. 12.3 Damping Stencils
    4. 12.4 Numerical Examples
    5. 12.5 Coefficients of Several Large Buffer Stencils
    6. 12.6 Large Buffer Selective Damping Stencils
    7. Exercises
  19. 13. Complex Geometry
    1. 13.1 Basic Concept of Overset Grids
    2. 13.2 Optimized Multidimensional Interpolation
    3. 13.3 Numerical Examples: Scattering Problems
    4. 13.4 Sliding Interface Problems
    5. Exercises
  20. 14. Continuation of a Near-Field Acoustic Solution to the Far Field
    1. 14.1 The Continuation Problem
    2. 14.2 Surface Green's Function: Pressure as the Matching Variable
    3. 14.3 Surface Green's Function: Normal Velocity as the Matching Variable
    4. 14.4 The Adjoint Green's Function
    5. 14.5 Adjoint Green's Function for a Conical Surface
    6. 14.6 Generation of a Random Broadband Acoustic Field
    7. 14.7 Continuation of Broadband Near Acoustic Field on a Conical Surface to the Far Field
    8. Exercise
  21. 15. Design of Computational Aeroacoustic Codes
    1. 15.1 Basic Elements of a CAA Code
    2. 15.2 Spatial Resolution Requirements
    3. 15.3 Mesh Design: Body-Fitted Grid
    4. 15.4 Example I: Direct Numerical Simulation of the Generation of Airfoil Tones at Moderate Reynolds Number
    5. 15.5 Computation of Turbulent Flows
    6. 15.6 Example II: Numerical Simulation of Axisymmetric Jet Screech
  22. Appendix A: Fourier and Laplace Transforms
  23. Appendix B: The Method of Stationary Phase
  24. Appendix C: The Method of Characteristics
  25. Appendix D: Diffusion Equation
  26. Appendix E: Accelerated Convergence to Steady State
  27. Appendix F: Generation of Broadband Sound Waves with a Prescribed Spectrum by an Energy-Conserving Discretization Method
  28. Appendix G: Sample Computer Programs
  29. References
  30. Index