自由项对交通流双曲型方程组数值解影响研究

该文以交通流模型中不同平衡函数表达式为例，对一阶非线性双曲型方程组的自由项形式与数值解的色散性、耗散性之间关系，进行了数值模拟研究。结果发现：自由项对方程组数值解的色散性和耗散性影响都是比较有规律的，这种规律性在不同初始密度条件下是不一样的；自由项导致方程组数值解色散或耗散强弱，与方程组的离散方式也有关，尤其在中等密度条件下。就Payne-Whitham模型方程，建议了能够对不同初始密度下扰动的传播和发展进行合理数值模拟的自由项和离散方式。

The influence of free term on the numerical solution of nonlinear first order hyperbolic equations

It is conducted that a numerical simulation research based on the examples of different types of balanced function in traffic flow model, explores the relationship between the type of free term and the dispersivity dissipation of the numerical solution of nonlinear first order equations of hyperbolic type. The result of the research shows that the influence of free term on the dispersivity dissipation of the numerical solution is regular, and the regularity is different under the different conditions of initial density; and the influence of free term on the dispersivity dissipation of numerical solution is related to the discrete way of the equations, especially under the condition of medium initial density. This paper also proposes the free term and discrete way which can conduct reasonable numerical simulation on the spreading and developing of disturbance under different conditions of initial density based on the equation of Payne-Whitham model.