In this work, we deal with collimated outflows of magnetized astrophysical plasma known as astrophysical jets, which have been observed to emerge from a wide variety of astrophysical compact objects. The latter systems can be considered as either hydrodynamic (HD) or magnetohydrodynamic (MHD) in nature, which means that they are governed by non-linear partial differential equations. In some of these systems, the velocity of the jet is very high and they require relativistic MHD (RMHD) treatment. We mainly focus on the appropriate numerical solutions of the MHD (and/or RMHD) equations as well as the transfer equation inside the jet and simulate multi-messenger emissions from specific astrophysical compact objects. We use a steady state axisymmetric model assuming relativistic magnetohydrodynamic descriptions for the jets (astrophysical plasma outflows) and perform numerical simulations for neutrino, gamma-ray and secondary particle emissions. By adopting the existence of such jets in black hole microquasars (and also in AGNs), the spherical symmetry of emissions is no longer valid, i.e., it is broken, and the system needs to be studied accordingly. One of the main goals is to estimate particle collision rates and particle energy distributions inside the jet, from black-hole microquasars. As concrete examples, we choose the Galactic Cygnus X-1 and the extragalactic LMC X-1 systems.