A hybrid scheme for solving a multi-class traffic flow model with complex wave breaking

Abstract

This paper extends the δ -mapping algorithm to solve a multi-class traffic flow model on an inhomogeneous highway, which is characterized by spatially varying fluxes and very complex waves. In the algorithm, the values of solution variables are mapped onto an intermediate state locally around the cell interface, and then the finite difference WENO reconstruction is applied. The hybrid scheme is consistent with steady flows, and resolves the waves more efficiently than the standard WENO scheme. The algorithm is also applicable to hyperbolic conservation laws with spatially varying fluxes in general.