Interactive synthesis of physical sound effects is crucial in digital media production. Sound radiation simulation, a key component of physically based sound synthesis, has posed challenges in the context of complex object boundaries. Previous methods, such as ghost cell-based finite-difference time-domain (FDTD) wave solver, have struggled to address these challenges, leading to large errors and failures in complex boundaries because of the limitation of ghost cells. We present SonicRadiation, a hybrid numerical solution capable of handling complex and dynamic object boundaries in sound radiation simulation without relying on ghost cells. We derive a consistent formulation to connect the physical quantities on grid cells in FDTD with the boundary elements in the time-domain boundary element method (TDBEM). Hereby, we propose a boundary grid synchronization strategy to seamlessly integrate TDBEM with FDTD while maintaining high numerical accuracy. Our method holds both advantages from the accuracy of TDBEM for the near-field and the efficiency of FDTD for the far-field. Experimental results demonstrate the superiority of our method in sound radiation simulation over previous approaches in terms of accuracy and efficiency, particularly in complex scenes, further validating its effectiveness.