Abstract: Large dense crowds show aggregate behavior with reduced individual freedom of movement. We present a novel, scalable approach for simulating such crowds, using a dual representation both as discrete agents and as a single continuous system. In the continuous setting, we introduce a novel variational constraint called unilateral incompressibility, to model the large-scale behavior of the crowd, and accelerate inter-agent collision avoidance in dense scenarios. This approach makes it possible to simulate very large, dense crowds composed of up to a hundred thousand agents at near-interactive rates on desktop computers.