The Lagrangian coordinate system and what it means for two-dimensional   crowd flow models
  A continuum crowd flow model is reformulated in the Lagrangian coordinate system. The system has proven to give computational advantages over the traditional Eulerian coordinate system for (one-dimensional) road traffic flow. Our extension of the model and simulation method to (two-dimensional) crowd flow paves the way to explore whether the advantages also hold in two dimensions. This paper provides a first exploration and shows that a model and simulation method for two-dimensional crowd flow can be developed in the Lagrangian coordinate system and that is leads to promising results. 
Femke van Wageningen-Kessels, Ludovic Leclercq, Winnie Daamen and   Serge P. Hoogendoorn
math.NA