We present three-dimensional hydrodynamic simulations of the evolution of self-gravitating, thick accretion discs around hyperaccreting stellar-mass black holes. The black hole-torus systems are considered to be remnants of compact object mergers, in which case the disc is not fed by an external mass reservoir and the accretion is non-stationary. Our models take into account viscous dissipation, described by an α-law, a detailed equation of state for the disc gas, and an approximate treatment of general relativistic effects on the disc structure by using a pseudo-Newtonian potential for the black hole including its possible rotation and spin-up during accretion. Magnetic fields are ignored. The neutrino emission of the hot disc is treated by a neutrino-trapping scheme, and the vv-annihilation near the disc is evaluated in a post-processing step. Our simulations show that the neutrino emission and energy deposition by vv-annihilation increase sensitively with the disc mass, with the black hole spin in case of a disc in corotation, and in particular with the α-viscosity. We find that for sufficiently large α-viscosity, vv-annihilation can be a viable energy source for gamma-ray bursts.