@Article{cmes.2011.079.237,
AUTHOR = {Durgesh  Vikram, Sanjay  Mittal, Partha  Chakroborty},
TITLE = {A Stabilized Finite Element Formulation for Continuum Models of Traffic Flow},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {79},
YEAR = {2011},
NUMBER = {3&4},
PAGES = {237--260},
URL = {http://www.techscience.com/CMES/v79n3&4/25744},
ISSN = {1526-1506},
ABSTRACT = {A stabilized finite element formulation is presented to solve the governing equations for traffic flow. The flow is assumed to be one-dimensional. Both, PW-type (Payne-Whitham) 2-equation models and the LWR-type (Lighthill-Whitham-Richards) 1-equation models are considered. The SUPG (Streamline-Upwind/Petrov-Galerkin) and shock capturing stabilizations are utilized. These stabilizations are sufficient for the 1-equation models. However, an additional stabilization is necessary for the 2-equation models. For the first time, such a stabilization is proposed. It arises from the coupling between the two equations and is termed as IEPG (Inter-Equation/Petrov-Galerkin) stabilization. Two behavioral models are studied: Greenshields' (<i>GS</i>) and Greenberg's (<i>GB</i>) models. Numerical tests are carried out for cases involving traffic expansion as well as shock. Excellent agreement with the exact solution is observed. The need of the IEPG stabilization for the 2-equation traffic models is demonstrated. An interesting observation is made for the first time regarding the Greenberg's (GB) model in the presence of a shock. The model is found to be inconsistent in the sense that it leads to different shock speed from the continuity and behavior equations. As a result, the 2-equation model leads to secondary waves in the presence of shocks.},
DOI = {10.3970/cmes.2011.079.237}
}