[en] A multi-velocity formulation for the solution of an Eulerian representation of an inert, disperse, and dilute particle-phase of a multi-phase flow is presented. Single velocity formulations are capable of predicting regions of zero particle concentration but are problematic with crossing particle trajectories or compression waves. The multi-velocity formulation described here can account for crossing particle trajectories by splitting the particle phase into distinct velocity families which are advected separately in the flow. Switching of the particle families at solid boundaries and due to momentum transfer with the gas-phase is conducted in a manner that enforces conservation of mass, momentum, and energy. This numerical method is combined with a parallel block-based adaptive mesh refinement algorithm that is very effective in treating problems with disparate length scales. The block-based data structure lends itself naturally to domain decomposition and thereby enables efficient and scalable implementations of the algorithm on distributed-memory multi-processor architectures. Numerical results are described to demonstrate the capabilities of the approach for predicting gas-particle flows. (author)