ZHANG Peng, WANG Zhuo, S.C.Wong. Fluid Dynamics Traffic Flow Models and Their Related Non-Linear Waves[J]. Applied Mathematics and Mechanics, 2013, 34(1): 85-97. doi: 10.3879/j.issn.1000-0887.2013.01.009
Citation: ZHANG Peng, WANG Zhuo, S.C.Wong. Fluid Dynamics Traffic Flow Models and Their Related Non-Linear Waves[J]. Applied Mathematics and Mechanics, 2013, 34(1): 85-97. doi: 10.3879/j.issn.1000-0887.2013.01.009

Fluid Dynamics Traffic Flow Models and Their Related Non-Linear Waves

doi: 10.3879/j.issn.1000-0887.2013.01.009
  • Received Date: 2012-11-19
  • Rev Recd Date: 2012-12-10
  • Publish Date: 2013-01-15
  • Fluid dynamics methods were used in modeling traffic flow problems, which demonstrated many interesting nonlinear propagation phenomena. It was summarized that the propagation was related to traffic pressures and self-driven forces, which generated shock and rarefaction waves in the LWR model, stop-and-go waves in the higher-order model, overtaking waves (shock or rarefaction waves) in the multi-class LWR model, and a contact discontinuity in problems with discontinuous fluxes. The Riemann problem arising from extension of the LWR model to traffic networks was also introduced in detail. And a system based on the Navier-Stokes equations was proposed to model the 2-dimensional pedestrian flow problem with application of the Eikon equation for determination of a pedestrian’s desired motion direction.
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