  We present a simple modification of the direct-forcing immersed boundary
method (IBM) proposed by Uhlmann [J. Comput. Phys, 2005] in order to enable it
to be applied to particulate flows with solid-to-fluid density ratios around
unity. The main difference with respect to the original formulation lies in the
particle velocity update which is performed directly after the preliminary
velocity field has been computed in the absence of any IBM volume forcing term.
In addition, we apply the forcing term to the entire space occupied by the
immersed solid object (instead of to the vicinity of its interface only). The
present approach requires the evaluation of integrals of the velocity field
over the volume occupied by the solid particle, which are evaluated efficiently
as sums over the respective quantities available at particle-attached force
points. The resulting method can be used seamlessly for density ratios down to
$\rho_p/\rho_f>0.5$. The new formulation has been validated using three
configurations: (i) lateral migration of a neutrally buoyant circular particle
in two-dimensional Couette flow; (ii) the release from rest of a neutrally
buoyant sphere in a free stream; (iii) the release of a particle in a free
stream after an initial phase in which it is translationally fixed with an
imposed angular velocity. In all three test cases the present IBM formulation
yields a very good agreement with the available reference data. Thus, the
proposed approach is a cost-efficient and accurate modification of the original
method which allows for the simulation of fluid systems involving
density-matched solid particles.
