Computer simulation of dense crowds is finding increased use in event planning, congestion prediction, and threat assessment. State-of-the-art particle-based crowd methods assume and aim for collision-free trajectories. That is an idealistic yet not overly realistic expectation, as near-collisions increase in dense and rushed settings compared with typically sparse pedestrian scenarios. Centroidal particle dynamics (CPD) is a method we defined that explicitly models the compressible personal space area surrounding each entity to inform its local pathing and collision-avoidance decisions. We illustrate how our proposed agent-based method for local dynamics can reproduce several key emergent dense crowd phenomena at the microscopic level with higher congruence to real trajectory data and with more visually convincing collision-avoidance paths than the existing state of the art. We present advanced models in which we consider distraction of the pedestrians in the crowd, flocking behavior, interaction with vehicles (ambulances, police) and other advanced models that show that emergent behavior in the simulated crowds is similar to the behavior observed in reality. We discuss how to increase confidence in CPD, potentially making it also suitable for use in safety-critical applications, including urban design, evacuation analysis, and crowd-safety planning.