Finite element analysis of freeway dynamics

A finite element methodology is presented for the numerical solution of problems encountered in freeway traffic flow. The purely dynamic traffic flow model consisting of the equations of continuity and momentum is adopted in this work. Both existing momentum equations are considered. A Galerkin type finite element method is used to discretize the problem in space and the solution is obtained by the two step Lax and Wendroff method applied in the time domain. The proposed finite element methodology which is of the shock capturing type, is applied to typical uninterrupted and interrupted freeway flow problems. Comparisons between the results obtained by the proposed methodology and ther numerical schemes as well as the results obtained by microscopic simulation are made. The results show that the present finite element methodology, at least in the example treated here, is not as fast and as accurate as the finite difference methodology that has been previously developed by the authors. The merits and deficiencies of the dynamic (high order continuum) models as compared with the simple continuum model are also assessed.