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Generalization of Runge‐Kutta discontinuous Galerkin method to LWR traffic flow model with inhomogeneous road conditions
Author(s) -
Zhang Peng,
Liu RuXun
Publication year - 2005
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20023
Subject(s) - runge–kutta methods , generalization , mathematics , limiter , discontinuous galerkin method , galerkin method , flow (mathematics) , partial differential equation , simple (philosophy) , flux limiter , extension (predicate logic) , flux (metallurgy) , function (biology) , mathematical analysis , traffic flow (computer networking) , differential equation , finite element method , geometry , computer science , physics , telecommunications , philosophy , materials science , epistemology , evolutionary biology , biology , metallurgy , thermodynamics , programming language , computer security
The discussed model is characterized by changeable lane numbers and free flow velocities that give rise to the spatially varying flux function in conservation equation. Accordingly a new numerical flux and a new limiter for the Runge‐Kutta Discontinuous Galerkin method are considered, which are compared with a natural but simple extension. It is verified that the new generalization is of high‐resolution and has wider stable and convergent ranges. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005