非等间距显式算法在重力波非线性传播数值模拟中的初步应用

Initial Application of Unequal Step Grid and Explicit Method in the Simulation of Nonlinear Propagation of Gravity Wave

采用3阶TVD型显式时间积分方法,建立了2维可压缩大气中重力波非线性传播的非等间距显式数值模式．对小振幅重力波传播过程的模拟结果表明,该模式能够很好地再现小振幅重力波的传播过程,并能保持能量守恒关系和各扰动量之间的相位关系,与线性重力波理论预测的结果吻合很好．对有限振幅重力波的模拟结果表明,与格点数相同的等间距网格中的模拟结果相比,采用非等间距网格能够以更高的分辨率模拟重力波的不稳定传播直到破碎的整个过程;在非等间距网格中的模拟结果与在加密一倍的等间距网格中的模拟结果相同,说明了用非等间距网格模拟重力波的饱和与破碎过程是正确的,并且采用非等间距网格能够大大减少计算量．

An unequal step grid and explicit numerical model is developed in this paper by using the 3rd order TVD explicit time integration method, which is used to simulate the nonlinear propagation of the gravity wave in a 2-dimensional compressible atmosphere. The model can simulate the small-scale complex wave with high resolution while the computer cost doesn＇t increase. It can be used to simulate the nonlinear propagation of gravity waves breaking into small-scale complex wave from the middle-scale wave. The simulation results for the propagation of small amplitude gravity wave indicate that, the model can reproduce the propagation of small amplitude gravity wave and preserve the energy conservation relation and the phase difference between different perturbation variable. The numerical results coincide well with linear gravity wave theory. The simulation results for the nonlinear propagation of finite amplitude gravity wave show that, compared with the equal grid system with the same grid number, the unequal step grid system can simulate the evolution of gravity wave from instable to breakdown with higher resolution. The simulation results in the equal grid system with the grid number increasing one time are same as that for the unequal grid system indicate that, the simulation results in the unequal grid system is correct, and the computer cost is saved greatly. The advantages of explicit method are also preserved in this model, such as, needn＇t iterative method to solve the solution and extend to 3-dimensional easily.