Computational Aeroacoustics

Short Course by PD Dr. Bernhard Müller

19 - 23 June 2006, 15.15 - 18.00 h, ETH Zürich, HG F 33.5

The objective of the short course is to illustrate the computation of sound waves. Computational Aeroacoustics (CAA) has only recently emerged as a new branch of Computational Fluid Dynamics (CFD). The technological challenge is due to more restrictive aerodynamic noise regulations for airplanes, helicopters, trains, cars, etc. The scientific challenge of CAA comes from the high accuracy demands over large space and time scales.

In the short course, the physical basics of sound wave propagation and sound wave generation will first be illustrated by deriving the wave equation and Lighthill's acoustic analogy from the continuity and momentum equations of fluid flow. Then, the use of Lighthill's acoustic analogy in conjunction with conventional CFD solutions will be briefly indicated to give an idea of classical CAA. Other acoustic analogies will be mentioned.

Instead of the wave equation, the linearized Euler equations have frequently been used to compute sound propagation, because they are not restricted to homogeneous media and can handle refraction and reflection of the sound waves. The linearized Euler equations will be derived from the conservation laws of mass, momentum and total energy for non-uniform compressible fluid flow.

For accurate wave simulations, fourth- or higher-order finite difference methods are more efficient than conventional second-order methods. Therefore, the advances of higher-order finite difference methods will be addressed. Methods with low dissipation and low dispersion errors will be explained. Near boundaries, the higher-order central methods are modified to satisfy a summation by parts property and thereby high order and strict stability. Boundary conditions can be prescribed by a penalty term called simultaneous approximation term.

The use of such higher-order finite difference methods for the linearized Euler equations and the nonlinear Euler and Navier-Stokes equations will be illustrated. Non-reflecting boundary conditions will receive special attention. Filtering of spurious modes and non-conservative formulations of the nonlinear equations will be mentioned.

The participants of the short course will have the opportunity to get practical experience in computing sound waves during four laboratory sessions on 19-22 June 2006, 17 - 18 h, in ML H41. Sample MATLAB programs will be provided.

The short course on CAA is intended for graduate students and people from academia and industry, who want to learn basics and advances of computing sound waves. The numerical issues will also be pertinent to the simulation of elastic and electromagnetic waves.

For information and registration, please contact the secretary of the Institute of Fluid Dynamics or mail to