A novel two-level space volume partition (SVP) algorithm based on the ray-tracing technique is proposed to predict the spatial distribution of the steady-state sound field. The sound space is subdivided into voxels in two levels. The voxels of the level-I are of greater size and comparable to the space walls, and the ray-wall intersection points are calculated based on this level of voxels. Then each level-I voxel is hierarchically subdivided into small voxels of level-II, the size of which is determined according to the needed solution in the sound field description. The sound field spatial distribution is predicted based on this level of voxels. A three-dimensional energy matrix is set up to memorize the spatial distribution of sound energy. The numbers of the row, column, and layer of the energy matrix are equal to those of the level-II voxels, namely, each element in the energy matrix corresponds to a level-II voxel. When a sound ray enters a voxel, its sound energy is calculated and recorded in the corresponding element of the energy matrix. When all the sound rays have been traced over, the sound energy spatial distribution in the sound space has been established in the energy matrix. The sound pressure level (SPL) in a certain plane or along a certain line can be calculated and imaged directly from the energy matrix. The novel two-level SVP algorithm can finish the simulation more efficiently than the traditional SVP algorithm. Experiments were performed to measure the SPL in steady-state sound fields, and the results were consistent with the predicted results.
Benchmark analytical solutions for steady state high frequency broadband sound fields in three rectangular enclosures