A maximum-principle-satisfying finite volume compact-WENO scheme for traffic flow model on networks

• In this paper, we apply a maximum-principle-satisfying nonlinear high order finite volume compact-WENO scheme to traffic flow problem on networks.
• The finite volume compact-WENO scheme is coupled with a limiter at each time stage to satisfy strict maximum principle under suitable CFL numbers.
• The numerical results demonstrate that the present compact-WENO scheme provided high resolution and essentially non-oscillatory numerical solutions.

In this paper, we apply a maximum-principle-satisfying finite volume compact weighted scheme to numerical modeling traffic flow problems on networks. Road networks can be numerically model as a graph, whose edges are a finite number of roads that join at junctions. The evolution on each road is described by a scalar hyperbolic conservation law, and traffic distribution matrices are used to formulate coupling conditions at the network junctions. In order to achieve maximum-principle of the traffic density on each road, the maximum-principle-satisfying polynomial rescaling limiter is adopted. Numerical results for road networks with rich solution structures are presented in this work and indicate that the finite volume compact weighted scheme produces essentially non-oscillatory, maximum principle preserving and high resolution solutions.