The fluid dynamics of a downer reactor were numerically resolved by adapting a mathematical conservation model. The mathematical model was based on the solid and fluid properties and physical characteristics using a cluster-based approach (CBA). Comparing the numerical results to the experimental data found in the literature indicated that the mathematical model could satisfactorily predict the experimental data. The mathematical simulation determined that there were three fluid dynamic areas in the downer reactor which were characterised by accelerated, slowed -down and fully-developed flow. The fully developed flow area in the downer decreased with increased gas surface speed keeping solid flux constant.