Explicit Construction of Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Non-Smooth Flow-Density Relationship
Abstract
In this paper, we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, continuous, concave, but not differentiable at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piecewise constant boundary conditions. As observed traffic flow data can be well fitted with such continuous piecewise quadratic functions, the explicitly constructed solutions provide a fast and accurate solution tool which may be used for predicting traffic or as a diagnosing tool to test the performance of numerical schemes. We implement these explicit entropy solutions for three representative traffic flow cases and also compare them with numerical solutions obtained by a high order weighted essentially non-oscillatory (WENO) scheme.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2006
- Accession Number
- ADA458956
Entities
People
- Chi-Wang Shu
- Mengping Zhang
- So C. Wong
- Wenqin Chen
- Yadong Lu
Organizations
- University of Science and Technology of China