Deterministic particle approximation of scalar conservation laws
  In this paper we prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. The result is complemented with some numerical simulations. 
Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini
math.AP