TY - JOUR
T1 - Impacts of Down-Up Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow
AU - Hu , Zejing
AU - Smirnova , M. N.
AU - Smirnov , N. N.
AU - Zhang , Yongliang
AU - Zhu , Zuojin
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1315
EP - 1334
PY - 2023
DA - 2023/06
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0316
UR - https://global-sci.org/intro/article_detail/aamm/21778.html
KW - Down-up hill road segment, viscoelastic continuum model, sags' bottleneck effect, density threshold, WENO5 scheme.
AB - <p style="text-align: justify;">The study of impacts of down-up hill road segment on the density threshold
of 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 gradient
increases gradually in the traffic direction. The main aim of this paper is to seek the
density threshold of shock formation of vehicular flow in ring road with down-up hill
segment, 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 threshold
numerically, a viscoelastic continuum model [1] is extended and used. To solve the
model equations, a fifth-order weighted essentially non-oscillatory scheme for spatial
discretization, and a 3rd order Runge-Kutta scheme for time partial derivative term
are used. Validation by existing observation data and the Navier-Stokes like model [2]
extended as EZM is done before conducting extensive numerical simulations. For ring
road vehicular flow with three separated down-up hill segments, it is found that the
density 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.</p>