To address the difficulties in reconstructing transient acoustic fields within a moving medium, an improved convective time-domain equivalent source method is proposed. This method is formulated based on the discretized integral solutions of the scalar and vector convective time-domain Ffowcs Williams–Hawkings equations utilizing monopole source terms. By matching acoustic pressure and particle velocity values at collocation points on an unenclosed sampling surface to the temporal derivatives of equivalent source strengths, a transfer matrix is constructed at each sampling time to progressively determine the unknown source strengths. The joint input of acoustic pressure and three Cartesian components of particle velocity significantly enhances reconstruction accuracy and reduces the number of required sampling points compared to pressure-only methods. Furthermore, a second-order central difference scheme combined with Lagrange linear interpolation is employed to accurately characterize the relationship between source strengths and their temporal derivatives. Additionally, the unphysical assumption that equivalent source strengths vanish prior to the initial source time is removed to capture historical contributions. The method's effectiveness and robustness are validated through numerical test cases in a uniform flow, including steady monopole and dipole sources, and an unsteady composite source.
Wang et al. (Sun,) studied this question.