An improved time-dependent Boundary Element Method for two-dimensional acoustic problems in a subsonic uniform flow

In this paper, we have developed an improved formulation of two-dimensional Convected Boundary Element Method (CBEM) for radiation and propagation acoustic problems in a uniform mean flow with arbitrary orientation. The improved CBEM approach is derived from an advanced form of time-space two-dimensional Boundary Integral Equation (BIE) according to new Sommerfeld Radiation Conditions (SRC) with arbitrary mean flow. The acoustic variables of these formulations are expressed only in terms of the acoustic field as well as its normal and tangential derivatives. The multiplication operators are based explicitly on the two-dimensional Green's function and its convected normal derivative kernel. The proposed terms significantly reduce the presence of flow quantities incorporated in the classical integral formulations. Precisely, the convected kernel only requires the evaluation of two terms instead of several terms in conventional formulations due to the flow effects in the temporal and spatial derivatives. Also, for the singular integrations, the kernels containing logarithmic and weak singularities are converted to regular forms and evaluated partially analytically and numerically. The formulation is derived to be easy to implement as a numerical tool for computational codes of acoustic mediums with arbitrary mean flow. The accuracy and robustness of this technique is assessed through several examples such as the two-dimensional monopole, dipole and quadrupole sources in a uniform mean flow. An application of the improved formulation coupled with Particular Dirichlet-to-Neumann operators (PDtN) has been presented to describe the acoustic field inside two-dimensional infinite ducts in a uniform mean flow. The numerical results are compared to analytical, conventional BEM and Finite Element Method (FEM) formulations.