Cross-comparison of numerical schemes for macroscopic traffic flow models

The aim of this paper is threefold. For one, we present a new computation scheme for the numerical approximation of solutions of Payne-type models. This scheme is proven to satisfy the positive constraints of traffic variables and thus prevents traffic from moving upstream. Secondly, we propose an automated model calibration approach, which is applied to determine the parameters of the considered macroscopic model for different numerical schemes (Steger-Warming, MacCormack, and the proposed numerical scheme). Thirdly, we will cross-compare the different calibrated numerical approximation models by comparing model predictions with observations from the validation dataset. Based on this cross-comparison, we conclude that the proposed numerical scheme is both more accurate and more robust than the other schemes considered. It yields a small mean squared error, fast computation due to the ability to use a larger time step, and also provides accurate results in regions where the gradients of the speeds and densities are high.