  Hot, tenuous advection-dominated accretion flows around black holes are ideal
sites for the Fermi acceleration of relativistic particles at standing shock
waves in the accretion disc. Previous work has demonstrated that the
shock-acceleration process can be efficient enough to power the observed,
strong outflows in radio-loud active galaxies such as M87. However, the
dynamical effect (back-reaction) on the flow, exerted by the pressure of the
relativistic particles, has not been previously considered, and this effect can
have a significant influence on the disc structure. We reexamine the problem by
developing a new, two-fluid model for the structure of the accretion disc that
includes the dynamical effect of the relativistic particle pressure, combined
with the pressure of the background (thermal) gas. The new model is analogous
to the two-fluid model of cosmic ray acceleration in supernova-driven shock
waves. As part of the model, we also develop a new set of shock jump
conditions, which are solved along with the hydrodynamic conservation equations
to determine the structure of the accretion disc. The solutions include the
formation of a mildly relativistic outflow (jet) at the shock radius, driven by
the relativistic particles accelerated in the disc. One of our main conclusions
is that in the context of the new two-fluid accretion model, global smooth
(shock-free) solutions do not exist, and the disc must always contain a
standing shock wave, at least in the inviscid case considered here.
