Computational Aeroacoustics A Wave Number Approach

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.

1. Finite difference equations; 2. Spatial discretization in wave number space; 3. Time discretization; 4. Finite difference scheme as dispersive waves; 5. Finite difference solution of the Euler equations; 6. Radiation, outflow, and wall boundary conditions; 7. The short wave component of finite difference schemes; 8. Nonlinear acoustic waves and shocks; 9. Advanced numerical boundary treatments; 10. Time domain impedance boundary condition; 11. Extrapolation and interpolation; 12. Multi-scales problems; 13. Complex geometry; 14. Continuation of a near field acoustic solution to the far field; 15. CAA code design and applications.

Dr Christopher Tam is the Robert O. Lawton Distinguished Professor in the Department of Mathematics at Florida State University. His research in computational mathematics and numerical simulation involves the development of low dispersion and dissipation computation schemes, numerical boundary conditions and the mathematical analysis of the scheme's computational properties for use in large scale numerical simulation of a number of real-world problems. Additionally he is developing jet and other aircraft noise theories as well as prediction codes for NASA and the US aircraft industry's noise reduction effort.