Traffic flow continuum modeling by hypersingular boundary integral equations

The quantity of data necessary in order to study traffic in dense urban areas through a traffic network, and the large volume of information that is provided as a result, causes managerial difficulties for the said model. A study of this kind is expensive and complex, with many sources of error connected to each step carried out. A simplification like the continuous medium is a reasonable approximation and, for certain dimensions of the actual problem, may be an alternative to be kept in mind. The hypotheses of the continuous model introduce errors comparable to those associated with geometric inaccuracies in the transport network, with the grouping of hundreds of streets in one same type of link and therefore having the same functional characteristics, with the centralization of all journey departure points and destinations in discrete centroids and with the uncertainty produced by a huge origin/destination matrix that is quickly phased out, etc. In the course of this work, a new model for characterizing traffic in dense network cities as a continuous medium, the diffusion-advection model, is put forward. The model is approached by means of the boundary element method, which has the fundamental characteristic of only requiring the contour of the problem to be discretized, thereby reducing the complexity and need for information into one order versus other more widespread methods, such as finite differences and the finite element method. On the other hand, the boundary elements method tends to give a more complex mathematical formulation. In order to validate the proposed technique, three examples in their fullest form are resolved with a known analytic solution. Copyright (C) 2009 John Wiley & Sons, Ltd.