  Astrophysical shocks create cosmic rays by accelerating charged particles to
relativistic speeds. However, the relative contribution of various types of
shocks to the cosmic ray spectrum is still the subject of ongoing debate.
Numerical studies have shown that in the non-relativistic regime, oblique
shocks are capable of accelerating cosmic rays, depending on the Alfv\'enic
Mach number of the shock. We now seek to extend this study into the mildly
relativistic regime. In this case, dependence of the ion reflection rate on the
shock obliquity is different compared to the nonrelativistic regime. Faster
relativistic shocks are perpendicular for the majority of shock obliquity
angles therefore their ability to initialize efficient DSA is limited. We
define the ion injection rate using fully kinetic PIC simulation where we
follow the formation of the shock and determine the fraction of ions that gets
involved into formation of the shock precursor in the mildly relativistic
regime covering a Lorentz factor range from 1 to 3. Then, with this result, we
use a combined PIC-MHD method to model the large-scale evolution of the shock
with the ion injection recipe dependent on the local shock obliquity. This
methodology accounts for the influence of the self-generated or pre-existing
upstream turbulence on the shock obliquity which allows study substantially
larger and longer simulations compared to classical hybrid techniques.
