Asymptotic limits of Riemann solutions to a novel second-order continuous macroscopic traffic flow model

The complete set of exact solutions to the Riemann problem for a novel second-order continuous macroscopic traffic flow model proposed by Hwang and Yu (J Comput Phys 350:927-950, 2017) is constructively solved in explicit forms by choosing the specific driving function of momentum. Especially, a hyperbolic composite wave is found in certain Riemann solution under the suitable initial condition, where a delta contact discontinuity is attached on the head of a rarefaction wave. Moreover, the asymptotic behavior of different Riemann solutions is explored and discussed, respectively, to analyze the influence of the two perturbed parameters in this model comprehensively. Additionally, the offered numerical experiments are well identical with our theoretic results.