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The code HARM\_COOL, a conservative scheme for relativisticmagnetohydrodynamics, is being developed in our group and works with atabulated equation of state of dense matter. This EOS can be chosen and usedduring dynamical simulation, instead of the simple ideal gas one. In this case,the inversion scheme between the conserved and primitive variables is not atrivial task. In principle, the code needs to solve numerically five couplednon-linear equations at every time-step. The 5-D recovery schemes wereoriginally implemented in HARM and worked accurately for a simple polytropicEOS which has an analytic form. Our current simulations support thecomposition-dependent EOS, formulated in terms of rest-mass density,temperature and electron fraction. In this proceeding, I discuss and compareseveral recovery schemes that have been included in our code. I also presentand discuss their convergence tests. Finally, I show set of preliminary resultsof a numerical simulation, addressed to the post-merger system formed after thebinary neutron stars (BNS) coalescence.

Neutrino cooled disk in post-merger system studied via numerical GR MHD simulation with a composition-dependent equation of state