Central finite volume schemes for non-local traffic flow models with Arrhenius-type look-ahead rules

Abstract

We present a central finite volume method and apply it to a new class of nonlocal traffic flow models with an Arrhenius-type look-ahead interaction. These models can be stated as scalar conservation laws with nonlocal fluxes. The suggested scheme is a development of the Nessyah–Tadmor non-oscillatory central scheme. We conduct several numerical experiments in which we carry out the following actions: i) we show the robustness and high resolution of the suggested method; ii) we compare the equations' solutions with local and nonlocal fluxes; iii) we examine how the look-ahead distance affects the numerical solution.