  In volume-filtered Euler-Lagrange simulations of particle-laden flows, the
fluid forces acting on a particle are estimated using reduced models, which
rely on the knowledge of the local undisturbed flow for that particle. Since
the two-way coupling between the particle and the fluid creates a local flow
perturbation, the filtered fluid velocity interpolated to the particle location
must be corrected prior to estimating the fluid forces, so as to subtract the
contribution of this perturbation and recover the local undisturbed flow with
good accuracy. In this manuscript, we present a new model for estimating a
particle's self-induced flow disturbance that accounts for its transient
development and for inertial effects related to finite particle Reynolds
numbers. The model also does not require the direction of the momentum feedback
to align with the direction of the particle's relative velocity, allowing force
contributions other than the steady drag force to be considered. It is based
upon the linearization of the volume-filtered equations governing the
particle's self-induced flow disturbance, such that their solution can be
expressed as a linear combination of regularized transient Stokeslet
contributions. Tested on a range of numerical cases, the model is shown to
consistently estimate the particle's self-induced flow disturbance with high
accuracy both in steady and highly transient flow environments, as well as for
finite particle Reynolds numbers.
