Year: 2019
Author: Raimund Bürger, Héctor Torres, Carlos A. Vega
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1022–1047
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0189
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1022–1047
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Multiclass Lighthill-Whitham-Richards traffic model system of conservation laws entropy conservative flux entropy stable scheme.
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