Consider a physical model (convection/reaction/diffusion of passive pollutant) and a city of characteristic length L. The smallest detail to be taken into account has length l< In this talk we present the basics of the method and its adaptation to urban transport of pollution. Indeed the key point is the choice of these basis functions and, more precisely, the internal boundary conditions on the coarse cells that one has to "guess". We will show that an oversampling technique is mandatory to avoid numerical artifacts. Moreover we will show through a penalisation method that the mesh does not have to exactly fit the complex topography of the city: it may be a structured Cartesian mesh which further improves the efficiency of the method. Through 2D satelite image of urban area we will show how to: - reconstruct an advection field (wind) given few meteorological data sites within the city, and - simulate the transport of pollution after an emergency situation (explosion, accident). Comparisons will be performed against the fine scale computation in terms of accuracy and efficiency.

Host: Mikhail Shashkov