Bart Bergen

Spline-based boundaries: A first step towards generic geometric domain descriptions for efficient mid-frequency acoustic analysis using the Wave Based Method

The application of numerical simulation techniques for the analysis and optimization of the acoustic behavior of all kinds of products has become very important in almost every phase of a design process. The large computational burden associated with the Finite Element Method (FEM) limits its applicability to low-frequency problems. Recently, the Wave Based Method (WBM) was proposed as an efficient alternative to the element based methods. This method is based on an indirect Trefftz approach, using an expansion of exact solutions of the governing differential equation to describe the dynamic field variables. An important disadvantage of the WBM is the limited geometrical flexibility as compared to the element based techniques. This paper aims to alleviate the geometrical restrictions by using B-splines for the efficient description of curved edges. The introduction of B-splines within the WBM requires an adaptation of the numerical integration procedure used to evaluate the weighted residual formulation. To this end, different types of numerical integration techniques are studied: the Gauss-Legendre and the Romberg integration procedure. A comparative study with the finite element method and the original WBM indicates that the application of B-splines and the adapted numerical integration procedure leads to accurate and computationally affordable WB models.

Coupling of Boundary Element and Wave Based Methods for the efficient solution of complex multiple scattering problems

A novel hybrid method for the efficient solution of complex acoustic multiple scattering problems is proposed in this paper. The Wave Based Method and the Boundary Element Method are coupled to benefit from the strengths of both. The former is an indirect Trefftz approach, which has a faster convergence rate and lower computational load compared to element based methods when applied on geometries of moderate complexity. The latter is the state-of-the-art technique for unbounded acoustic problems and can handle very complex geometries. The idea behind the hybrid method is to take advantage of the fast WBM solution for scatterers of moderate complexity and take advantage of the BEM@?s capability for handling scatterers of high complexity. For the BEM part, the indirect variational formulation is used which allows modeling of open boundary problems (zero thickness walls). In addition, the WBM makes it possible to easily add heterogeneities (domain inclusions) to the problem. Therefore, the hybrid method does not only aim for better efficiency but also for extending the variety of configurations that can be tackled by both methods with ease. The accuracy and the performance of the method are demonstrated with three examples, both in 2D and 3D. It is shown that when complex and simple scatterers coexist, the hybrid method is more efficient than the WBM, the BEM and the Fast-Multipole BEM while it is able to provide accuracy of similar level.

A novel modelling approach for sound propagation analysis in a multiple scatterer environment

In the past decades element‐based numerical modelling techniques have become a commonly used and invaluable tool for the analysis of acoustic radiation and scattering problems. However, the pollution errors associated with the element discretisation inherent to these methods increase with the increasing size of the problem domain. As a result, the applicability of these methods for radiation and scattering problems in which the source and receiver positions are located far from each other is often prohibited. The Wave Based Method (WBM) is an alternative deterministic prediction method for the analysis of steady‐state acoustic problems. It is based on an indirect Trefftz approach in that wave functions, which are exact solutions of the underlying differential equation, are used to describe the dynamic response. The enhanced computational efficiency of the WBM as compared to the element based methods has been shown already for the analysis of both finite and (semi‐)infinite acoustic problems. This paper introduces a novel WBM‐based methodology to model the acoustic source‐receiver transfer path functions in a multiple scatterer environment. A sound propagation validation case illustrates the potential of the proposed approach.