A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid （CLEAR-VOF） method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.
Aiming at the real-time fluctuation and nonlinear characteristics of the expressway short-term traffic flow forecasting the parameter projection pursuit regression PPPR model is applied to forecast the expressway traffic flow where the orthogonal Hermite polynomial is used to fit the ridge functions and the least square method is employed to determine the polynomial weight coefficient c.In order to efficiently optimize the projection direction a and the number M of ridge functions of the PPPR model the chaos cloud particle swarm optimization CCPSO algorithm is applied to optimize the parameters. The CCPSO-PPPR hybrid optimization model for expressway short-term traffic flow forecasting is established in which the CCPSO algorithm is used to optimize the optimal projection direction a in the inner layer while the number M of ridge functions is optimized in the outer layer.Traffic volume weather factors and travel date of the previous several time intervals of the road section are taken as the input influencing factors. Example forecasting and model comparison results indicate that the proposed model can obtain a better forecasting effect and its absolute error is controlled within [-6,6] which can meet the application requirements of expressway traffic flow forecasting.
