An optically thin advective accretion disk is crucial for explaining the hard state of black hole sources. Using general relativistic magnetohydrodynamic (GRMHD) simulations, we investigate how a large-scale, strong magnetic field influences accretion and outflows/jets, depending on the field geometry, magnetic field strength, and the spin parameter of the black hole. We simulate a sub-Eddington, advective disk-outflow system in the presence of a strong magnetic field, which likely remains in the hard state. The model simulations based on HARMPI successfully explain ultra-luminous X-ray sources (ULXs) in the hard state, typically observed with luminosities ranging from \(10^{39}\) – \(10^{40}\) ergs s \(^{-1}\) . Our simulations generally describe the bright, hard state of stellar-mass black hole sources without requiring a super-Eddington accretion rate. This chapter explores the characteristics of ULXs without invoking intermediate-mass black holes. The observed high luminosity is attributed to the energy stored in the strong magnetic fields, which can generate super-Eddington luminosity. The combined energy of the matter and magnetic field leads to such significant luminosity.