有限差分格式与物理量守恒性  

A COMPARISON BETWEEN FINITE DIFFERENCE SCHEMES AND PHYSICAL CONSERVATION FEATURES

作　　者：季仲贞[1] 王斌[1] 杨诗芳[1] 

机构地区：[1]中国科学院大气物理研究所大气科学与地球流体力学数值模拟国家重点实验室,北京100029

出　　处：《地球物理学报》2004年第6期991-996,共6页Chinese Journal of Geophysics

基　　金：国家重点基础研究发展规划项目 ( 973 ) (G19990 3 2 80 1);国家科技攻关项目 ( 2 0 0 1BA60 3B 0 4;2 0 0 1BA60 7B0 )

摘　　要：为了成功地开展大气数值模拟 ,如何构造相应的离散格式是一项十分重要的工作 .本文以大气球面浅水方程为例 ,从不同形式的微分方程组出发 ,分别构造了能量守恒格式、准辛格式和多守恒格式 ,并作相应的数值检验和比较 ,从中可以清楚地看到三类格式的优劣 .这三类格式构造方法不同 ,所保持的物理守恒性不完全相同 ,数值计算时所需机时也不同 。It is a key issue for successful atmospheric numerical simulations that how to construct the relatively efficient discrete schemes of the original problem. In this paper the spherical shallow water equations are taken as an example to address this issue. Three schemes, i.e., (i) an explicit energy conservation scheme, (ii) a sympletic-like scheme, and (iii) a multi-conservation scheme, are constructed for the equations in different partial differential forms, respectively. Numerical tests show that these different difference schemes conserve the different strongpoints and shortcomings in physical conservation properties and numerical costs because of the different scheme constructions, which provide choice basis of algorithms according to the real application.

关 键 词：球面浅水方程 物理量守恒 总能量守恒格式 准辛格式 多守恒格式 

分 类 号：P401[天文地球—大气物理学与大气环境]