Three-dimensional numerical simulations of gas dynamics are used to study the flow pattern in a close binary system after it has reached the steady-state accretion regime. It is shown that an additional spiral density wave can exist in the inner parts of the cold accretion disk, where gas-dynamical perturbations are negligible. This spiral wave is due to the retrograde precession of the flowlines in the binary system. It is found that shape and position of a substantial part of the disk are specified by a precessional density wave. On timescales comparable to the orbital period, the precessional wave (and hence an appreciable fraction of the disk) will be virtually stationary in the observer’s frame, whereas the positions of other elements of the flow will vary due to the orbital rotation. The periodic variations of the positions of the disk and the bow shock formed when the inner parts of the circumbinary envelope flow around the disk result in variations of both the rate of angular-momentum transfer to the disk and the flow structure near the Lagrange point L3. All these factors lead to a periodic increase of the matter flow into the outer layers of the circumbinary envelope through the vicinity of L3.

Tidal disruption by massive black holes is a phenomenon, during which a large part of gravitational energy can be released on a very short time-scale. The time-scales and energies involved during X-ray and IR flares observed in Galactic centre suggest that they may be related to tidal disruption events. Furthermore, aftermath of a tidal disruption of a star by super-massive black hole has been observed in some galaxies, e.g. RX J1242.6-1119A. All these discoveries increased the demand for tools for tidal disruption study in curved space-time. Here we summarise our study of general relativistic effects on tidal deformation of stars and compact objects.