Mertens T., Bouillard P., Astley J., Gamallo P.

The Finite Element Method (FEM) is often used to solve numerical acoustic applications. However, it has been noticed that the computational resources increase dramatically with the excitation frequency. Applications such as the noise radiated from the inlet of an airplane engine motivates the need for improved numerical methods. In this paper, an Infinite Partition of Unity Method (IPUM) is implemented to study axisymmetric applications. The formulation is based on the convected wave equation so that it takes into account the effect of non-uniform flows on acoustic propagation. The concept of Infinite Elements developed by Astley [1] is used to deal with unbounded fluids. The domain is first decomposed in an inner and an outer region. The PUM is then used in the inner region while the outer one is discretized by a finite number of Partition of Unity Infinite Elements. The speciality of the PUM is that the shape functions can be constructed such that they correspond to a better approximation of the physics. This code allows the use of both polynomial and trigonometric enrichments. We first introduce the theory and then illustrate some characteristics of the method through convergence simulations on academic examples where the analytic solution is known. The results are also compared to FEM solutions. The radiation of a turbofan will be treated to show the applicability of the method to industrial problems. [1] R. Astley, G. Macaulay, J-P. Coyette, L. Cremers, “Three-dimensional wave-envelope elements of variable order for acoustic radiation and scattering. Part I. Formulation in the frequency domain”, Journal of Acoustical Society of America, Vol. 103, No. 1, 1998, pp. 49-63.