采用隐式立方样条计算平流过程的数值模式及理想实验

A Numerical Model of Solving Advaction Equation by the Implicit Cubic Spline Method and the Numerical Experiments

本文介绍了一种用隐式立方样条求解平流方程的数值方法,并从理论上对其无条件稳定性进行了证明,在此基础上建立了一个在地形坐标系下的两维原始方程模式,模式在行星边界层参数化中引入了湍流动能方程,在模式顶部引入了吸收层.数值实验表明:模式有较好的计算稳定性,对较高的模式水平分辨率和复杂地形均有较强的适应能力;对复杂地形和下垫面非均匀热源条件下中尺度系统的模拟能获得合理的结果,并具有较高的精确度.

In this paper, an implicit cubic spline scheme is adopted to solve the advection equation. Its non-conditionally linear stability is proved. Based on this scheme, a two dimensional numerical model with an upper absorbing layer and a turbulent energy equation based on the turbulent closure have been developed in a terrain following coordinate.Several numerical experiments are carried out. The reasonable results show that the model is suitable for modeling and studying topographical forcing and induced mesoscale systems with sat -isfactory, accuracy, computational stability and flexibility for model's horizontal resolution and complex topography.