An Exact and Grid-free Numerical Scheme for the Hybrid Two Phase Traffic Flow Model Based on the Lighthill-Whitham-Richards Model with Bounded Acceleration
AdvisorsClaudel, Christian G.
KAUST DepartmentPhysical Science and Engineering (PSE) Division
Embargo End Date2013-07-30
Permanent link to this recordhttp://hdl.handle.net/10754/245871
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Access RestrictionsAt the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis became available to the public after the expiration of the embargo on 2013-07-30.
AbstractIn this article, we propose a new grid-free and exact solution method for computing solutions associated with an hybrid traffic flow model based on the Lighthill- Whitham-Richards (LWR) partial differential equation. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a fixed acceleration otherwise. We first present a grid-free solution method for the LWR equation based on the minimization of component functions. We then show that this solution method can be extended to compute the solutions to the hybrid model by proper modification of the component functions, for any concave fundamental diagram. We derive these functions analytically for the specific case of a triangular fundamental diagram. We also show that the proposed computational method can handle fixed or moving bottlenecks.