  Aims: We have developed a new code for the three-dimensional time-dependent
raditation hydrodynamic simulation of the stellar wind in interacting binaries
to improve models of accretion in high-mass X-ray binaries and to
quantitatively clarify the observed variability of these objects. We used the
code to test the influence of various parameters on the structure and
properties of circumstellar matter. Methods: Our code takes into account
acceleration of the wind due to the Roche effective potential, Coriolis force,
gas pressure, and (CAK-) radiative pressure in the lines and continuum of the
supergiant radiation field that is modulated by its gravity darkening and by
the photo-ionization caused by X-ray radiation from the compact companion. The
parameters of Cygnus X-1 were used to test the properties of our model.
Results: Both two- and three-dimensional numerical simulations show that the
Coriolis force substantially influences the mass loss and consequently the
accretion rate onto the compact companion. The gravitational field of the
compact companion focuses the stellar wind, which leads to the formation of a
curved cone-like gaseous tail behind the companion. The changes of X-ray
photo-ionization of the wind material during X-ray spectral-state transitions
significantly influence the wind structure and offer an explanation of the
variability of Cygnus X-1 in optical observations (the H$\alpha$ emission).

Solar and Stellar Astrophysics