Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics
Alexander Kurganov - Mathematics Department, Tulane University, New Orleans, LA 70118, United States (email)
We first develop non-oscillatory central schemes for a traffic flow model with Arrhenius look-ahead dynamics, proposed in [ A. Sopasakis
and M.A. Katsoulakis, SIAM J. Appl. Math., 66 (2006), pp. 921--944]. This model takes into account interactions of every vehicle with other
vehicles ahead ("look-ahead'' rule) and can be written as a one-dimensional scalar conservation law with a global flux. The proposed schemes
are extensions of the non-oscillatory central schemes, which belong to a class of Godunov-type projection-evolution methods. In this framework,
a solution, computed at a certain time, is first approximated by a piecewise polynomial function, which is then evolved to the next time level
according to the integral form of the conservation law. Most Godunov-type schemes are based on upwinding, which requires solving (generalized)
Riemann problems. However, no (approximate) Riemann problem solver is available for conservation laws with global fluxes. Therefore, central
schemes, which are Riemann-problem-solver-free, are especially attractive for the studied traffic flow model. Our numerical experiments
demonstrate high resolution, stability, and robustness of the proposed methods, which are used to numerically investigate both dispersive and
smoothing effects of the global flux.
Keywords: traffic flow, scalar conservation law with a global flux,
non-oscillatory central schemes, finite volume methods, Arrhenius
Received: April 2008; Revised: February 2009; Published: July 2009.
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