Volume 11, Issue 5
An Entropy Stable Scheme for the Multiclass Lighthill-Whitham-Richards Traffic Model

Raimund Bürger, Héctor Torres & Carlos A. Vega

Adv. Appl. Math. Mech., 11 (2019), pp. 1022-1047.

Published online: 2019-06

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  • Abstract

An entropy conservative (EC) numerical flux for the  multiclass Lighthill-Whitham-Richards (MCLWR) kinematic traffic model  based on the  general framework by Tadmor [E. Tadmor, The numerical viscosity of entropy stable schemes for systems of conservation laws, I,  Math. Comput.,  49 (1987), pp. 91--103] is proposed. The approach exploits the  existence of an entropy pair for a particular form of this model.  The  construction of EC  fluxes is of interest since in combination  with numerical diffusion terms they allow  one  to design  entropy stable schemes for the MCLWR model. In order to obtain a higher-order accurate scheme and control oscillations near discontinuities, a third-order WENO reconstruction recently proposed  by Ray [D. Ray,  Third-order entropy stable scheme for the compressible Euler equations, in  C. Klingenberg and M. Westdickenberg (eds.), Springer Proc. Math. Stat., 237, pp. 503--515] is used.  Numerical experiments for different classes of drivers are presented to test the performance of the entropy stable scheme constructed with the entropy conservative flux proposed.

  • Keywords

Multiclass Lighthill-Whitham-Richards traffic model, system of conservation laws, entropy conservative flux, entropy stable scheme.

  • AMS Subject Headings

35L65, 35L45, 765M06, 6T99, 90B20

  • Copyright

COPYRIGHT: © Global Science Press

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