Numerical stabilities and boundary conditions in time-domain Eulerian simulations of acoustic wave propagations with and without background flow

A thorough numerical analysis is performed for time-domain simulation of acoustic wave propagations in the atmosphere, with the ground modeled as a porous medium. Two types of computational grid arrangement for the simulation, i.e., the staggered grid and the collocated grid, are considered. It is proved that the computational schemes based on these two grids are identical under certain finite differencing procedures. The numerical stability analysis is studied that applies to both of the grids. Non-reflecting, absorbing boundary conditions are used at the free-space boundary. Simulations on the collocated grid are then carried out for a model problem of sound propagation in the air/ground to confirm the equivalency of the two grids and to investigate the effectiveness of non-reflecting boundary conditions. The results are compared with the data in the literature and with bench-mark simulation, and very good agreements have been achieved.