  The code HARM\_COOL, a conservative scheme for relativistic
magnetohydrodynamics, is being developed in our group and works with a
tabulated equation of state of dense matter. This EOS can be chosen and used
during dynamical simulation, instead of the simple ideal gas one. In this case,
the inversion scheme between the conserved and primitive variables is not a
trivial task. In principle, the code needs to solve numerically five coupled
non-linear equations at every time-step. The 5-D recovery schemes were
originally implemented in HARM and worked accurately for a simple polytropic
EOS which has an analytic form. Our current simulations support the
composition-dependent EOS, formulated in terms of rest-mass density,
temperature and electron fraction. In this proceeding, I discuss and compare
several recovery schemes that have been included in our code. I also present
and discuss their convergence tests. Finally, I show set of preliminary results
of a numerical simulation, addressed to the post-merger system formed after the
binary neutron stars (BNS) coalescence.
