利用谱方法数值求解三维球坐标系下的Navier-Stokes方程  

A Spectral Numerical Solution of Navier-Stokes Equations in a 3-Dimensional Spherical Coordinate System

作　　者：黄春明[1] 易帆[1] 张绍东[1] 

机构地区：[1]武汉大学电子信息学院,武汉430079

出　　处：《空间科学学报》2005年第1期37-43,共7页Chinese Journal of Space Science

基　　金：国家自然科学基金重点项目(40336054)国家自然科学基金项目(40274051)共同资助

摘　　要：从三维球坐标系下的 Navier-Stokes 方程出发，采用谱配置方法建立了一个三维球坐标系下中层大气波动传播的全非线性动力学数值模式；构造了合理的纬向边界，并利用初始给定的重力波波包对该模式进行了数值检验．计算结果展示了重力波波包在大气中传播的三维图像，波包整体向上传播，波相关扰动速度随高度的增加而增长．Aiming at numerically studying the global nonlinear propagation of atmospheric tides,anew fully nonlinear numerical model in a three dimensional spherical coordinates is established.In theconstruction of the numerical model,the spectral allocation method was used to numerically resolvethe Navier-Stokes equations,which was taking as the governing equations.In the specification of theboundary conditions,periodic and projected characteristic line boundaries are chosen as the zonaland vertical boundaries,respectively;moreover,the polar boundary are also carefully specified.Forthe purpose of examining our newly established model,the global nonlinear propagation of a gravity-wave packet with large scales is simulated and compared with a previou simulation.The calculationresult exhibits the essential characteristics of the nonlinear propagation of a gravity-wave packet inatmosphere:the whole wave packet propagates upward and the wave-associated disturbance velocityincreases with the increasing height,which is quantitatively consistent with the previous simulation.These suggested that our numerical model and the nonlinear simulation are reliable.

关 键 词：NAVIER-STOKES方程 球坐标系 谱方法 数值求解 重力波波包 三维 扰动 中层大气 数值模式 构造 

分 类 号：P401[天文地球—大气物理学与大气环境]