A Cheap and Easy-to-Implement Upwind Scheme for Second Order Traffic Flow Models

We extend the finite volume numerical scheme proposed by Hilliges and Weidlich [11] to second order traffic flow models consisting in \(2\times 2\) systems of non strictly hyperbolic conservation laws of Temple class. The scheme is shown to satisfy some maximum principle properties on the density. We provide numerical tests illustrating the behaviour at vacuum and the gain in computational time when dealing with optimization algorithms.