A High Resolution Finite Volume Scheme For Traffic Flow On Networks

This paper is based on the LWR model theory and aims to solve the hyperbolic conservation law equation of traffic flow density under different road network structures.The exact solution of this kind of equation is difficult to get directly,and some appropriate numerical scheme is usually used to determine the numerical solution of the equation.However,even if the given initial conditions are sufficiently smooth,the numerical solution may be discontinuous at some time.When the high order scheme is used to solve the equation,the numerical oscillation may occur near the discontinuity.In this paper,we will use the finite volume method and Hermite interpolation primary function to construct a HRUS high-resolution bounded scheme that can satisfy both convection boundedness criterion condition and total variational diminishing constraint.Then we use this scheme to simulate five typical traffic flow problems.Comparing the numerical results with the reference solutions,it is found that the scheme can effectively suppress non-physical oscillations near the discontinuities and maintain a good performance of numerical approximation.