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Conservation form of Helbing’s fluid dynamic traffic flow model. (English) Zbl 1237.76072
Summary: A standard conservation form is derived in this paper. The hyperbolicity of Helbing’s fluid dynamic traffic flow model is proved, which is essential to the general analytical and numerical study of this model. On the basis of this conservation form, a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently. The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated. This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients, and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.
MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
35Q35 PDEs in connection with fluid mechanics
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