  Suspension flows are ubiquitous in nature (hemodynamics, subsurface fluid
mechanics, etc.) and industrial applications (hydraulic fracturing, CO$_2$
storage, etc.). However, such flows are notoriously difficult to model due to
the variety of fluid-particle and particle-particle interactions that can
occur. In this work, we focus on non-Brownian shear-dominated suspensions,
where kinetic collisions are negligible and frictional effects play a dominant
role. Under these circumstances, irreversible phenomena such as particle
diffusion and migration arise, requiring anisotropic stress models to describe
the suspension rheology. On a continuum level, reduced-order models such as the
suspension balance model (SBM) or the diffusive flux model are commonly used to
predict particle migration phenomena. We propose a new method based on a
two-fluid model (TFM), where both the phases are considered as interpenetrating
continua with their own conservation of mass and momentum equations. Without
employing the nowadays customary simplifications in applying the SBM, we close
the ``full'' TFM instead. Specifically, we show that when an anisotropic stress
analogous to that used in the SBM is added to the equilibrium equations for the
particle phase, the TFM is able to accurately predict particle migration. Thus,
the TFM does not require the assumptions of a steady suspension velocity and a
Stokesian (inertialess) fluid, and the TFM can be easily extended to include
buoyancy and even kinetic collisional models. We present several benchmark
simulations of our TFM implementation in
OpenFOAM{\textsuperscript\textregistered}, including in curvilinear coordinates
and three-dimensional flow. Good agreement between the TFM solutions and
previous experimental and numerical results is found.
