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Second-Order Traffic Flow Models on Networks
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2021-02-22 , DOI: 10.1137/20m1339908 Simone Göttlich , Michael Herty , Salissou Moutari , Jennifer Weissen
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2021-02-22 , DOI: 10.1137/20m1339908 Simone Göttlich , Michael Herty , Salissou Moutari , Jennifer Weissen
SIAM Journal on Applied Mathematics, Volume 81, Issue 1, Page 258-281, January 2021.
This paper deals with the Aw--Rascle--Zhang [A. Aw and M. Rascle, SIAM J. Appl. Math., 60 (2000), pp. 916--938; H. M. Zhang, Transp. Res. B Methodol., 36 (2002), pp. 275--290] model for traffic flow on uni-directional road networks. We construct weak solutions to Riemann problems at the junctions, which conserve the mass and the generalized momentum. In particular, we introduce a new approach to approximate the homogenized pressure through an additional equation for the propagation of a reference pressure. The resulting system of coupled conservation laws is then solved using an appropriate numerical scheme of Godunov type. Numerical simulations show that the proposed approach enables us to approximate the homogenized pressure sufficiently well. The features of the new approach are illustrated through a comparative analysis with other methods proposed in the literature for the Aw--Rascle--Zhang second-order traffic model [2, 31] and the Lighthill--Whitham--Richards model [M. J. Lighthill and G. B. Whitman, Proc. A, 229 (1955), pp. 317--345; P. I. Richards, Oper. Res., 4 (1956), pp. 42--51].
更新日期：2021-03-03
This paper deals with the Aw--Rascle--Zhang [A. Aw and M. Rascle, SIAM J. Appl. Math., 60 (2000), pp. 916--938; H. M. Zhang, Transp. Res. B Methodol., 36 (2002), pp. 275--290] model for traffic flow on uni-directional road networks. We construct weak solutions to Riemann problems at the junctions, which conserve the mass and the generalized momentum. In particular, we introduce a new approach to approximate the homogenized pressure through an additional equation for the propagation of a reference pressure. The resulting system of coupled conservation laws is then solved using an appropriate numerical scheme of Godunov type. Numerical simulations show that the proposed approach enables us to approximate the homogenized pressure sufficiently well. The features of the new approach are illustrated through a comparative analysis with other methods proposed in the literature for the Aw--Rascle--Zhang second-order traffic model [2, 31] and the Lighthill--Whitham--Richards model [M. J. Lighthill and G. B. Whitman, Proc. A, 229 (1955), pp. 317--345; P. I. Richards, Oper. Res., 4 (1956), pp. 42--51].
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