This paper concerns the numerical modeling of heavy particle motion in a turbulent flow. Instantaneous fluid velocity is simulated by low-order dynamical systems based on Proper Orthogonal Decomposition (POD), or the eigenfunction expansion, which is a mathematical tool that can be used to identify the most energetic structures of the flow. The POD basis was built using two-point velocity correlations obtained from the Direct Numerical Simulation (DNS) of a channel flow. In addition to the two proposals already described from the literature, a new dynamical system with considerably less modes was constructed. The dynamical systems were assessed by comparing the resulting fluid velocity statistics with the DNS data. The Lagrangian approach was used to track inertial particles, which were one-way coupled to the velocity field generated by these dynamical systems. In the dispersion study, where the particles are allowed to collide elastically with the walls, the particle number density profiles and velocity statistics were compared to the available DNS benchmark. In the case of particle wall separation, the results for deposition velocity were evaluated with experimental data. The characteristic features of the POD-based simulations of dispersed turbulent flows are shown, potential areas of application are suggested, and the limitations of the approach are discussed. (C) 2013 Elsevier Ltd. All rights reserved.