An isogeometric Burton-Miller method for the transmission loss optimization with application to mufflers with internal extended tubes

In this work, the problem of a muffler with internal extended inlet/outlet tubes is studied with the aim to optimize its geometric design. When boundary element method (BEM) based on the conventional boundary integral equation (CBIE) is used for structures with thin walls (internal extended tubes of small thickness), it produces nearly singular integrals which require smaller elements and higher number of Gauss quadrature points to maintain sufficient accuracy of the overall solution. An alternative approach, known as mixed or dual BEM, which consists of neglecting the tube thickness, models the wall as a single surface and prescribes BIEs of different types on each side. However, this alternative leads to some discrepancies in the obtained results compared to other numerical or experimental data especially at higher frequencies. Another approach in this work is to utilize Burton-Miller method (BM) prescribing a combination of two types of BIEs on the original thin-walled geometry. BM is introduced in the framework of isogeometric analysis (IGA) to solve the muffler problem as an interior 3D Helmholtz acoustic problem producing more accurate results. In addition, the isogeometric BM (IGA-BM) model benefits from the BEM philosophy of reducing the dimensionality of a 3D problem to consider only its surfaces/boundaries. Moreover, producing the 4-pole parameters of the transmission loss (TL) entering/exiting the inlet/outlet tubes is convenient in the framework of BEM, which easily predicts the physical variables on the problem boundary.