A Time-Domain Boundary Integral Equation for Moving Acoustic Sources in Uniform Flow and Its Solution by an Advanced Time Propagation Approach

This paper presents a time-domain boundary integral equation (TDBIE) formulation for predicting acoustic scattering from moving sources in a uniform mean flow. This work is motivated by the increasing need for accurate aeroacoustic modeling of modern aircraft configurations, including VTOL and eVTOL systems with rotating components. A key challenge in time-domain scattering simulations with moving sources is the determination of retarded time for a given observer time, which involves solving an implicit equation at each time step. This can be computationally costly, particularly for numerical solution of the TDBIE where every surface element on the scattering body acts as an observer. To address this, a Non-uniform Grid Interpolation Distribution Algorithm (NGIDA), which is a high-order accurate algorithm that avoids the need for solving retarded-time equations, is introduced. The high-order accuracy is beneficial for resolving acoustic waves at high frequencies. The method converts interpolation-based values from a non-uniform advanced time grid onto a uniformly spaced observer time grid. It achieves high-order accuracy while avoiding repeated evaluations of the acoustic signal, thereby significantly reducing memory requirements and computational cost. Numerical examples involving both rotational and rectilinear source motions are presented for validation. Scattering by rigid and lined flat plates is simulated, and results are shown to agree closely with analytical solutions, demonstrating the accuracy and efficiency of the proposed approach.