Towards steady-state solutions for supersonic wind accretion on to gravitating objects

We discuss the results of a numerical simulation of the hydrodynamic Bondi- Hoyle accretion obtained on the basis of a high-resolution numerical scheme with the proper entropy correction procedure necessary to avoid the 'weak' non-monotonicity intrinsic in these schemes. Both the axisymmetric and pla ne cases are considered. The axisymmetric accretion problem turns out to ha ve steady-state solutions for all determining parameters. Steady-state solu tions for the plane accretion are found in certain cases even for sinusoida lly perturbed and strongly non-uniform winds. Non-stationary phenomena do e xist but they are not very violent and can sometimes be attributed as well to numerical as to physical reasons.