Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model
نویسندگان
چکیده
The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density a(x) represents road inhomogeneities, such as variable numbers of lanes, and is allowed to vary discontinuously. The car density φ = φ(x, t) is then determined by the following initial value problem for a scalar conservation law with a spatially discontinuous flux:
منابع مشابه
On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux
Abstract. We study a system of conservation laws that describes multispecies kinematic flows with an emphasis on models of multiclass traffic flow and of the creaming of oil-in-water dispersions. The flux can have a spatial discontinuity which models abrupt changes of road surface conditions or of the cross-sectional area in a settling vessel. For this system, an entropy inequality is proposed ...
متن کاملContinuous kinematic wave models of merging traffic flow
Traffic dynamics at a merging junction can be numerically solved with discrete conservation equationsand so-called supply-demand methods. In this paper, we first introduce a continuous multi-commoditykinematic wave model of merging traffic and then develop a new framework for constructing the solutionsto its Riemann problem with jump initial conditions. In the supply-demand spac...
متن کاملThe Inhomogeneous Kinematic Wave Traffic Flow Model as a Resonant Nonlinear System
The kinematic wave traffic flow model for an inhomogeneous road is studied as a resonant nonlinear system, where an additional conservation law is introduced to model time-invariant road inhomogeneities such as changes in grades or number of lanes. This resonant system has two families of waves, one of which is a standing wave originated at the inhomogeneity. The nature of these waves are exami...
متن کاملL∞ Solutions for a Model of Polytropic Gas Flow with Diffusive Entropy
We establish the global existence of L∞ solutions for a model of polytropic gas flow with diffusive entropy. The result is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax– Friedrichs and Godunov schemes. Such convergence is achieved by proving the estimates required for the application of the compensated compactness theory.
متن کاملAdaptive multiresolution WENO schemes for Traffic Flow Problems
Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of firstorder, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill-Whitham-Richards traffic model [4] and a model for the sedimentation of polydisperse suspensions...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- NHM
دوره 3 شماره
صفحات -
تاریخ انتشار 2008