Splitting and merging technique is one of the effective refinement tools to increase the resolution in particle methods. However, it still has many challenges in stability, accuracy and conservation issues. In this research, a pair splitting technique with minimum density error, as well as with mass, momentum and energy conservations, is proposed. Instead of using a fixed splitting pattern adopted in previous researches, the splitting angle and distance in this research are dynamically obtained by achieving the total minimum density error of splitting particles and their surrounding particles. Regarding the merging algorithm, a triplet particle merging model with two small particles and one large particle is proposed to maintain angular momentum conservation. A minimum merging distance limitation is developed to ensure mass, momentum and energy conservations at the same time. A set of cases are investigated to validate the effectiveness, stability and conservation of the present splitting and merging model. The results show that the present model decreases large oscillations and avoids sudden disturb caused by irregular particle distribution due to splitting and merging.     «

Splitting and merging technique is one of the effective refinement tools to increase the resolution in particle methods. However, it still has many challenges in stability, accuracy and conservation issues. In this research, a pair splitting technique with minimum density error, as well as with mass, momentum and energy conservations, is proposed. Instead of using a fixed splitting pattern adopted in previous researches, the splitting angle and distance in this research are dynamically obtained...     »