  X-ray emission associated to accretion onto compact objects displays
important levels of photometric and spectroscopic time-variability. When the
accretor orbits a Supergiant star, it captures a fraction of the supersonic
radiatively-driven wind which forms shocks in its vicinity. The amplitude and
stability of this gravitational beaming of the flow conditions the mass
accretion rate responsible, in fine, for the X-ray luminosity of those
Supergiant X-ray Binaries. The capacity of this low angular momentum inflow to
form a disc-like structure susceptible to be the stage of well-known
instabilities remains at stake. Using state-of-the-art numerical setups, we
characterized the structure of a Bondi-Hoyle-Lyttleton flow onto a compact
object, from the shock down to the vicinity of the accretor, typically five
orders of magnitude smaller. The evolution of the mass accretion rate and of
the bow shock which forms around the accretor (transverse structure, opening
angle, stability, temperature profile) with the Mach number of the incoming
flow is described in detail. The robustness of those simulations based on the
High Performance Computing MPI-AMRVAC code is supported by the topology of the
inner sonic surface, in agreement with theoretical expectations. We developed a
synthetic model of mass transfer in Supergiant X-ray Binaries which couples the
launching of the wind accordingly to the stellar parameters, the orbital
evolution of the streamlines in a modified Roche potential and the accretion
process. We show that the shape of the permanent flow is entirely determined by
the mass ratio, the filling factor, the Eddington factor and the alpha-force
multiplier. Provided scales such as the orbital period are known, we can trace
back the observables to evaluate the mass accretion rates, the accretion
mechanism (stream or wind-dominated) and the shearing of the inflow.
