  The presence of a surface at the inner boundary, such as in a neutron star or
a white dwarf, allows the existence of a standing shock in steady spherical
accretion.The standing shock can become unstable in 2D or 3D; this is called
the {\em standing accretion shock instability} (SASI).Two mechanisms --
advective-acoustic and purely acoustic -- have been proposed to explain SASI.
Using axisymmetric hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations,
we find that the advective-acoustic mechanism better matches the observed
oscillation timescales in our simulations. The global shock oscillations
present in the accretion flow can explain many observed high frequency
($\gtrsim 100$ Hz) quasi-periodic oscillations (QPOs) in X-ray binaries (XRBs).
The presence of a moderately strong magnetic field adds more features to the
shock oscillation pattern, giving rise to low frequency modulation in the
computed light curve. This low frequency modulation can be responsible for
$\sim 100$ Hz QPOs (known as hHz QPOs). We propose that the appearance of hHz
QPO determines the separation of twin peak QPOs of higher frequencies.
