Three dimensional numerical simulations of acoustic wave field in the upper convection zone of the Sun

Results of numerical 3D simulations of propagation of acoustic waves inside the Sun are presented. A linear 3D code which utilizes realistic OPAL equation of state was developed by authors. Modified convectively stable standard solar model with smoothly joined chromosphere was used as a background model. High order dispersion relation preserving numerical scheme was used to calculate spatial derivatives. The top non-reflecting boundary condition established in the chromosphere absorbs waves with frequencies greater than the acoustic cut-off frequency which pass to the chromosphere, simulating a realistic situation. The acoustic power spectra obtained from the wave field generated by sources randomly distributed below the photosphere are in good agreement with observations. The influence of the height of the top boundary on results of simulation was studied. It was shown that the energy leakage through the acoustic potential barrier damps all modes uniformly and does not change the shape of the acoustic spectrum. So the height of the top boundary can be used for controlling a damping rate without distortion of the acoustic spectrum. The developed simulations provide an important tool for testing local helioseismology.