In this study, we present an equivalent second-order formulation of the LWR model based on Phillips’ model, in which the acceleration rate equals a relaxation term with an infinitesimal relaxation time. We convert the model into a continuum car-following model and demonstrate its equivalence to that of the LWR model. We demonstrate that the nonstandard second-order model is stable, but the original Phillips model is not. We derive conditions for the nonstandard model to be forward-traveling and collision-free, prove that the collision-free condition is consistent with but more general than the CFL condition, and demonstrate that only anisotropic and symplectic Euler discretization methods lead to physically meaningful solutions. Numerically, the nonstandard second-order model has the same shock and rarefaction wave solutions as the LWR model for both Greenshields and triangular fundamental diagrams; for a non-concave fundamental diagram, the collision-free condition, but not the CFL condition, yields physically meaningful results.
Nonstandard second-order formulation of the LWR model
Transportmetrica B: Transport Dynamics ; 7 , 1 ; 1338-1355
2019-12-23
18 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Reduced Order Solution of Nonstandard H~ Control Problem
British Library Online Contents | 1996
|Nonstandard ridehail use in Austin
Elsevier | 2020
|Nonstandard Recognition Problems in Seismology
British Library Online Contents | 1996
|On a nonstandard Lorentz invariant model of the photon
Online Contents | 2011
|On a nonstandard Lorentz invariant model of the photon
Elsevier | 2011
|