We derive new axially symmetric stationary solutions to the barotropic Euler equations with a body force in the isentropic and isothermal cases. They are used as the initial distributions in the related non-stationary problem. Basing on a quasi-hydrodynamic approach, we perform numerical experiments on the development of small initial perturbations of the azimuthal velocity and the formation of large structures like the density ''sleeves''. Splitting of the sleeves and decreasing of the gas angular momentum in the middle of the field are observed. Also the correctness of the shallow water approximation for describing the sleeve formation is confirmed. The designed algorithm is universal and allows one to perform various numerical experiments of interest in astrophysics on a personal computer.

gas dynamic equations, polar coordinates, stationary solutions, accretion disk, quasi-gas dynamic approach, finite-difference approximation, numerical experiments

Mathematical modelling in actual problems of science and technics

Elizarova Tatiana Gennadyevna,  ,  orcid.org/0000-0001-6169-5270,  KIAM RAS

Zlotnik Alexander Anatolyevich,  ,  НИУ Высшая школа экономики

Istomina Maria Alexandrovna,  ,  KIAM RAS