High-fidelity numerical simulations have been performed to study the formation and fragmentation of liquid sheets formed by two impinging jets using an improved volume-of-fluid (VOF) method augmented with several adaptive mesh refinement (AMR) techniques. An efficient topology-oriented strategy was further established to optimize the performance and accuracy of the AMR algorithm. Two benchmark cases pertaining to low- and high-velocity impinging jets are simulated as part of a grid refinement study. Calculated jet dynamics show excellent agreement with experimental observations in terms of the rim shape, droplet size distribution and impact wave structures. Detailed flow physics associated with the temporal evolution and spatial development of the jets are explored over a wide range of Reynolds and Weber numbers. A realistic rendering post-processing using a ray-tracing technique is performed to obtain direct insight to the flow evolution. Special attention is paid to the dynamics of the impact wave which dominates the atomization of the injected liquid. The work appears to be the first systematic numerical study in which all the flow patterns formed by impingement of two liquid jets are obtained. Fine structures are captured based on their characteristic length scales. Various atomization modes, from stable to highly unstable, are resolved with high fidelity.