Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing
SIAM Journal on Numerical Analysis
A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A moving mesh method with variable mesh relaxation time
Applied Numerical Mathematics
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In this paper, we describe a one-dimensional adaptive moving mesh method and apply it to the traffic flow model introduced in 2006 by Sopasakis and Katsoulakis and its modified model proposed in 2009 by Kurganov and Polizzi. These models can be written as a scalar conservation law with a global flux. The proposed scheme is an extension of the moving non-oscillatory central scheme, which belongs to a class of moving finite volume methods. We also modify the model given by Kurganov and Polizzi to account for the driver's reaction, i.e. delayed response. Finally, the moving finite volume method is extended accordingly.