Author:
Gowda G. D. Veerappa,Kenettinkara Sudarshan Kumar,Manoj Nikhil
Abstract
In this article, we present the convergence analysis of a second-order numerical scheme for traffic flow models that incorporate non-local conservation laws. We combine a MUSCL-type spatial reconstruction with strong stability preserving Runge-Kutta time-stepping to devise a fully discrete second-order scheme. The resulting scheme is shown to converge to a weak solution by establishing the maximum principle, bounded variation estimates and L1Lipschitz continuity in time. Further, using a space-step dependent slope limiter, we prove its convergence to the entropy solution. We also propose a MUSCL-Hancock type second-order scheme which requires only one intermediate stage unlike the Runge-Kutta schemes and is easier to implement. The performance of the proposed second-order schemes in comparison to a first-order scheme is demonstrated through several numerical experiments.
Funder
MATRICS- Government of India
Raja Ramanna, Government of India
Council of Scientific and Industrial Research (CSIR), Government of India,