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Authors 2019 Article in Periodical Astronomy and Astrophysics http://dx.doi.org/10.1051/0004-6361/201833429 http://dx.doi.org/10.1051/0004-6361/201833429 supernovae: general -- stars: mass-loss -- stars: circumstellar matter -- stars: evolution -- hydrodynamics Massive stars are characterized by a significant loss of mass either via (nearly) spherically symmetric stellar winds or pre-explosion pulses, or by aspherical forms of circumstellar matter (CSM) such as bipolar lobes or outflowing circumstellar equatorial disks. Since a significant fraction of most massive stars end their lives by a core collapse, supernovae (SNe) are always located inside large circumstellar envelopes created by their progenitors. We study the dynamics and thermal effects of collision between expanding ejecta of SNe and CSM that may be formed during, for example, a sgB[e] star phase, a luminous blue variable phase, around PopIII stars, or by various forms of accretion. For time-dependent hydrodynamic modeling we used our own grid-based Eulerian multidimensional hydrodynamic code built with a finite volumes method. The code is based on a directionally unsplit Roe's method that is highly efficient for calculations of shocks and physical flows with large discontinuities. We simulate a SNe explosion as a spherically symmetric blast wave. The initial geometry of the disks corresponds to a density structure of a material that orbits in Keplerian trajectories. We examine the behavior of basic hydrodynamic characteristics, i.e., the density, pressure, velocity of expansion, and temperature structure in the interaction zone under various geometrical configurations and various initial densities of CSM. We calculate the evolution of the SN - CSM system and the rate of aspherical deceleration as well as the degree of anisotropy in density, pressure, and temperature distribution. Our simulations reveal significant asphericity of the expanding envelope above all in the case of dense equatorial disks. Our low density'' model however also shows significant asphericity in the case of the disk mass-loss rate $\dot{M}_\text{csd}=10^{-6}\,M_\odot\,\text{yr}^{-1}$. The models also show the zones of overdensity in the SN - disk contact region and indicate the development of Kelvin-Helmholtz instabilities within the zones of shear between the disk and the more freely expanding material outside the disk.