We propose a new characteristic-based finite volume scheme combined with the method of Central Weighted Essentially Non-Oscillatory(CWENO) reconstruction and characteristics,to solve shallow water equations.We apply the scheme to simulate dam-break problems.A number of challenging test cases are considered,such as large depth differences even wet/dry bed.The numerical solutions well agree with the analytical solutions.The results demonstrate the desired accuracy,high-resolution and robustness of the presented scheme.
In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.
