May 23, 2016 — May 27, 2016
- Manfred Kaltenbacher (Vienna University of Technology, Vienna, Austria)
Noise levels have become an issue for urban communities for many years due to the rapid growth of
air and ground traffic densities (e.g., airplanes, trains, cars, etc.). Additionally to these noise sources, many other machines (e.g., wind turbines, pumps, fans, etc.) producing significant noise levels surround our daily activities and contribute to deterioration of quality of life. A quite large part of this noise is generated by vibrating structures and by ows (flow induced sound), and manufactures have considered the noise level of their products as a relevant design parameter. Therefore, the demand towards reliable and computational efficient numerical simulation programs is strongly growing, so that these tools can be used within a virtual prototyping development cycle.
The aim of the course is to present the state-of-the-art overview of numerical schemes efficiently solving the acoustic conservation equations (unknowns are acoustic pressure and particle velocity) and the acoustic wave equation (pressure or acoustic potential formulation). Thereby, the different equations model both vibrational and owinduced sound generation and its propagation. In addition, state-of-the-art methods for the solution of so-called inverse problems, i.e., problems of identifying sources, scatterers, material properties, etc., will be presented. Main applications, which will be discussed within the course, will be towards aerospace, rail and automotive industry as well as medical engineering. Thereby, we have composed a team of lecturers who are able to address these topics from the engineering as well as numerical points of view.
The course will contain both the physical / mathematical modelling, latest numerical schemes to solve the underlying partial differential equations, and relevant practical applications. Thereby, we will derive the conservation equations of acoustics both for a stagnant as well as moving uid. In addition, we will derive the couplings to structural mechanics and fluid flow. This will allow us to describe vibrational as well as flow induced (aeroacoustics) sound. In a next part, we will present appropriate numerical schemes for the solution of the derived partial differential equations: finite difference, finite element, finite volume, and boundary element methods. We will discuss latest numerical schemes as higher order and spectral finite elements, mixed finite elements, nonconforming grid techniques as well as discontinuous Galerkin methods. For many practical applications, one needs to apply impedance boundary conditions and has to cope with free radiation. Here, we will discuss higher order absorbing boundary conditions and perfectly matched layer techniques to efficiently approximate free radiation conditions. Since numerical schemes leads to a system of algebraic equations, which have to be solved, we will also present algorithms for direct and iterative solvers as well as latest developments on multigrid methods.
The course is addressed to doctoral students and postdoctoral fellows, as well as to academic and industrial researchers and practicing engineers, with a background in mechanics, acoustics, applied physics, aerospace engineering, civil engineering or applied mathematics.