Abstract: A system and method are introduced for simulating the particulate physical systems governed by population balance equations with particle splitting (breakage) and aggregation based on accurately conserving an unlimited number of moments associated with the particle size distribution. The basic idea is based on the concept of primary and secondary particles, where the former is responsible for the distribution reconstruction while the latter one is responsible for different particle interactions such as splitting and aggregation. The system and method are found to track accurately any set of low-order moments with the ability to reconstruct the shape of the distribution.