Features of SPH gas dynamics for modeling of nonlinear gravitational waves in multiphase medium

SPH is widely adopted to treat gas dynamics in astrophysical calculations. One of the most state-of-art problems is connected with testing codes based on this method and verification of nonstationary solutions provided by the codes. Description of developed SPH-code Sombrero and results of modeling of axi-symmetrical and radial-azimuth perturbations spreading in multiphase gravitational medium are presented in the article. By means of comparison of numerical results obtained using SPH and FLIC methods, we have demonstrated ability of SPH to reproduce nonlinear waves in gas-collisionless bodies' medium even if shear and cross-current flows take place in the system.