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Solitary wave solution to Aw-Rascle viscous model of traffic flow. (English) Zbl 1400.35200

Summary: A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.

MSC:

35Q35 PDEs in connection with fluid mechanics
35C07 Traveling wave solutions
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35C08 Soliton solutions
35L65 Hyperbolic conservation laws
35Q53 KdV equations (Korteweg-de Vries equations)
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References:

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