Impacts of Down-Up Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow (Advances in Applied Mathematics and Mechanics, 2023)
The study of impacts of down-up hill road segment on the density thresholdof traffic shock formation in ring road vehicular flow is helpful to the deep understanding of sags’ bottleneck effect. Sags are freeway segments along which the gradientincreases gradually in the traffic direction. The main aim of this paper is to seek thedensity threshold of shock formation of vehicular flow in ring road with down-up hillsegment, because down-up hill roadway segment is a source to cause capacity reduction that is an attractive topic in vehicular traffic science. To seek the density thresholdnumerically, a viscoelastic continuum model [1] is extended and used. To solve themodel equations, a fifth-order weighted essentially non-oscillatory scheme for spatialdiscretization, and a 3rd order Runge-Kutta scheme for time partial derivative termare used. Validation by existing observation data and the Navier-Stokes like model [2]extended as EZM is done before conducting extensive numerical simulations. For ringroad vehicular flow with three separated down-up hill segments, it is found that thedensity threshold of shock formation decreases monotonically with the relative difference of free flow speed, this variation can be simply fitted by a third order polynomial.