Boundary Element and Finite Element Coupling for Aeroacoustics Simulations

We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary.Comment: 25 page

An integral formulation for wave propagation on weakly non-uniform potential flows

An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green's function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green's function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results show that the error associated with the physical model deteriorates with increasing frequency and mean flow Mach number. However, the error is generated only in the domain where mean flow non-uniformities are significant and is constant in regions where the flow is uniform

A nonintrusive Reduced Basis Method applied to aeroacoustic simulations

The Reduced Basis Method can be exploited in an efficient way only if the so-called affine dependence assumption on the operator and right-hand side of the considered problem with respect to the parameters is satisfied. When it is not, the Empirical Interpolation Method is usually used to recover this assumption approximately. In both cases, the Reduced Basis Method requires to access and modify the assembly routines of the corresponding computational code, leading to an intrusive procedure. In this work, we derive variants of the EIM algorithm and explain how they can be used to turn the Reduced Basis Method into a nonintrusive procedure. We present examples of aeroacoustic problems solved by integral equations and show how our algorithms can benefit from the linear algebra tools available in the considered code.Comment: 28 pages, 7 figure

A nonintrusive method to approximate linear systems with nonlinear parameter dependence

We consider a family of linear systems $A_\mu \alpha=C$ with system matrix $A_\mu$ depending on a parameter $\mu$ and for simplicity parameter-independent right-hand side $C$. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form $A_\mu\approx\sum_{m}\beta_m(\mu)A_{\mu_m}$ for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices $A_{\mu_m}$. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.Comment: 17 pages, 9 figure

Extension of the concept of Ffowcs-Williams and Hawkings type wave extrapolation to non-trivial flow effects and exterieor surfaces

In appreciation of Ffowcs-Williams and Hawkings’ seminal contribution on describing the sound radiation from moving objects, this article discusses a concept of taking into account local non-trivial flow effects on the sound propagation. The approach is motivated by the fact that the numerical simulation of the sound propagation from complete full scale aircraft by means of volume-discretizing (CAA = Computational AeroAcoustics) methods is prohibitively expensive

The Boundary Element Method in Acoustics: A Survey

The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed. The basis of the BEM is initially developed for Laplace’s equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller’s equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised

Further developments on theoretical and computational rheology

Tese financiada pela FCT - Fundação para a Ciência e a Tecnologia, Ciência.Inovação2010, POPH, União Europeia FEDERTese de doutoramento. Engenharia Química e Biológica. Faculdade de Engenharia. Universidade do Porto. 201