  To study the dynamics of particles in turbulence when their sizes are
comparable to the smallest eddies in the flow, the Kolmogorov length scale,
efficient and accurate numerical models for the particle-fluid interaction are
still missing. Therefore, we here extend the treatment of the particle feedback
on the fluid based on the volume-averaged fluid equations (VA simulation) in
the previous study of the present authors, by estimating the fluid force
correlated with the disturbed flow. We validate the model against
interface-resolved simulations using the immersed-boundary method. Simulations
of single particles show that the history effect is well captured by the
present estimation method based on the disturbed flow. Similarly, the
simulation of the flow around a rotating particle demonstrates that the lift
force is also well captured by the proposed method. We also consider the
interaction between non-negligible size particles and an array of Taylor-Green
vortices. For density ratios $\rho_d/\rho_c\geq$ 10, the results show that the
particle motion captured by the VA approach is closer to that of the
fully-resolved simulations than that obtained with a traditional two-way
coupling simulation. The flow disturbance is also well represented by the VA
simulation. In particular, it is found that history effects enhance the
curvature of the trajectory in vortices and this enhancement increases with the
particle size. Furthermore, the flow field generated by a neighboring particle
at distances of around ten particle diameters significantly influences particle
trajectories. The computational cost of the VA simulation proposed here is
considerably lower than that of the interface-resolved simulation.
