  The accuracy of Lagrangian point-particle models for simulation of
particle-laden flows may degrade when the particle and fluid momentum equations
are two-way coupled. In these cases the fluid velocity at the location of the
particle, which is often used as an estimation of the undisturbed velocity, is
altered by the presence of the particle, modifying the slip velocity and
producing an erroneous prediction of coupling forces between fluid and
particle. In this article, we propose a correction scheme to eliminate this
error and predict the undisturbed fluid velocity accurately. Conceptually, in
this method, the computation cell is treated as a solid object immersed in the
fluid that is subjected to the two-way coupling force and dragged at a velocity
that is identical to the disturbance created by the particle. The proposed
scheme is generic as it can be applied to unstructured grids with arbitrary
geometry and particles that have different size and density. At its crudest
form for isotropic grids, the present correction scheme reduces to dividing the
Stokes drag by $1 - 0.75\Lambda$, where $\Lambda$ is the ratio of the particle
diameter to the grid size. The accuracy of the proposed scheme is evaluated by
comparing the computed settling velocity of individual and pair of particles
under gravity on anisotropic rectilinear grids against analytical solutions.
This comparison shows up to two orders of magnitude reduction in error in cases
where the particle is up to 5 times larger than the grid that may have an
aspect ratio of over 10. Furthermore, a comparison against the
particle-resolved simulation of decaying turbulence demonstrates the excellent
accuracy of the proposed scheme.
