中文摘要：

利用CIP（Constrained Interpolation Profile）特征线半拉格朗日解法对平面一维和二维浅水波方程的重力波和普通经纬度网格下的球面浅水波模式进行了数值求解试验,给出了CIP特征线法的数值结果和对应大时间步长积分的对比。结果显示,一维CIP特征线法对重力波的位相、振幅和传播有很好的描述,对于不同时间步长都显示出计算稳定的特性。空间分离的二维特征线法是多维问题计算中简单有效的方法,在平面和球面二维问题的数值结果中都得到了CIP特征线法稳定的计算和良好的波动传播结果,在浅水波方程中可以克服半隐式算法在高分辨率时的大量运算,并有望成为处理重力波的替代算法。

英文摘要：

The computation of gravity waves in atmospheric numerical model is important for the dynamical effect on weather system.The computing process is usually very expensive,and requests a lot of resources.In order to circumvent the computational instability and mass requirement of computer resources,characteristic CIP（Constrained Interpolation Profile） method is used to test the semi-Lagrangian computation of gravity wave in a 2-dimensional sphere in addition to 1 and 2-dimensional plains.The corresponding numerical results of short time steps with characteristic CIP method are shown in comparison with that of large Courant number.The 1-dimensional characteristic CIP method is shown bears strong computational stability,and gives precise wave phase,amplitude and the propagation speed.The dimensional splitting method is of simple and effective for multi-dimensional problem.Practical integration of 2-dimensional shallow water models in both Cartesian and spherical coordinates have illustrated nice performance,as well as strong computational stability.It successfully avoids the mass computation associated with semi-implicit integration of gravity waves in high-resolution case,and can be applied to shallow water model to deal with gravity wave.