  We describe an immersed boundary method in which the fluid-structure coupling
is achieved in an Eulerian framework. The method is an improved extension of
the immersed boundary method originally developed by Kajishima et al. [1],
which accounts for the inertia of the fictitious fluid inside the particle
volume and is thus able to reproduce the behaviour of particles both in the
case of neutrally-buoyant objects and in the presence of density difference
between the particles and the fluid. The method is capable to handle the
presence of multiple suspended objects, i.e., a suspension, by including a
soft-sphere normal collision model, while the lubrication correction typically
added to similar immersed boundary methods in order to capture the sub-grid
unresolved lubrication force is here treated implicitly, i.e., naturally
obtained without any explicit expression, thus no additional computation is
required. We show that our methodology can successfully reproduce the rheology
of a particle suspension in a shear flow up to a dense regime (with a maximum
particle volume fraction around 46%) without any additional correction force.
The applicability of this methodology is also tested in a turbulent
pressure-driven duct flow at high Reynolds number in the presence of
non-negligible inertia and non-uniform shear-rate, showing good agreement with
experimental measurements.
