This paper presents a computational methodology for the two and three dimensional numerical simulation of dense and dilute dispersed particles in multiphase gas-solid and liquid-solid flows. The model equations are based on the two fluids approximation, with closure terms for the fluid-solid drag interaction forces and the additional dense collisional terms arising from particle-particle interactions under the kinetic theory. These equations are discretized and solved using a novel unstructured mesh control volume-finite element framework, with an anisotropic mesh adaptivity capability. The methodology is applied to study the transport of sand particles of various sizes in fluidized beds, as well as particle segregation in a polydisperse system containing three solid particle sizes. (C) 2014 Elsevier Ltd. All rights reserved.