Pedestrian dynamics is an interdisciplinary field of research. Psychologists, sociologists, traffic engineers, physicists, mathematicians and computer scientists all strive to understand the dynamics of a moving crowd. In principle, computer simulations offer means to further this understanding. Yet, unlike for many classic dynamical systems in physics, there is no universally accepted locomotion model for crowd dynamics. On the contrary, a multitude of approaches, with very different characteristics, compete. Often only the experts in one special model type are able to assess the consequences these characteristics have on a simulation study. Therefore, scientists from all disciplines who wish to use simulations to analyze pedestrian dynamics need a tool to compare competing approaches. Developers, too, would profit from an easy way to get insight into an alternative modeling ansatz. Vadere meets this interdisciplinary demand by offering an open-source simulation framework that is lightweight in its approach and in its user interface while offering pre-implemented versions of the most widely spread models.

The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

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