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气象:1998,24(10):20-25
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半拉格朗日方法在全球原始方程模式中的实现
(国家气象中心,北京 100081)
Implementation of the Semi Lagrangian Method in the Primitive equations Model
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中文摘要: 简单介绍了半拉格朗日平流方案的基本概念,并详细总结了其在全球原始方程模式,特别是在IFS模式中的具体实现过程。拉格朗日平流的观点是跟着流体质点看流体运动,其实现的关键是流体轨迹的计算。轨迹中点和起始点水平坐标的求得可以利用球面三角,直接在球极坐标中进行,并采用一些较高的近似。为了充分获得半拉格朗日方案的益处,在起始点的内插公式其阶数至少应在四阶(三次)以上,为避免昂贵的三维三次内插,可以采用三维“准三次”内插。
Abstract:The basic concept of the Semi Lagrangian method was simply introduced,and then its concrete implementation in the primitive equations model,especially in IFS model was presented.The idea of the Lagrangian advection is that an observer watches the world evolve around him as he travels with a fluid particle,and the key to its implementation is the calculation of the trajectory.Taking advantage of the spherical trigonometry and a higher order approximation,the horizontal coordinates of the position for the midpoint and the departure point of the trajectory can be calculated directly in the spherical polar coordinates.To obtain the advantages of a semi Lagrangian integration scheme,it was necessary to choose the order of the interpolation higher than fourth order for the terms evaluated at the departure point.However,in order to avoid expensive cubic interpolation in three dimension,it was better to choose 3D "quasi cubic" interpolation.
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引用文本:
陈起英,庄世宇,金之雁,1998.半拉格朗日方法在全球原始方程模式中的实现[J].气象,24(10):20-25.
,1998.Implementation of the Semi Lagrangian Method in the Primitive equations Model[J].Meteor Mon,24(10):20-25.