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

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.