作　　者： ; ; ;

机构地区： 中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室

出　　处： 《气候与环境研究》 1999年第2期8-24,共17页

摘　　要： 为了适应发展气候数值模拟和环境数值模拟的需要，综合介绍了与此密切有关的若干计算问题。首先，指出这类问题易于出现计算紊乱、非物理解和非线性计算不稳定，同时，简要介绍造成这些问题出现的三种机理：虚假频散、能量关系破坏和能谱的非线性转移。然后，把这类问题归结为一种“发展方程”，给出了与此有关的几个定理，阐述了计算稳定性、能量守恒性和算子非负性之间的密切关系。接着，分别介绍了多种完全平方守恒的差分格式的构造方法，其中包括隐式的和显式的完全平方守恒的差分格式，高时间精度和高阶紧致的完全平方守恒的差分格式，同时也给出若干具体算例说明这些格式的计算效果。最后，对全文作了小结，并指出今后应进一步研究的若干重要问题。 In order to satisfy the requirement of developing climate and environment numerical simulation, several closely related computational problems are introduced in this paper First, computing chaos, nonphysical solutions, and nonlinear computational instability are often discovered in these problems At the same time three reasons that result in these problems are discussed These reasons are false dispersion, disconstruction of energy relationship, and nonlinear displacement of energy spectrum Then these problems are contributed to a kind of “evolution equation”, several related theorems are presented, and the relationship between computational stability, energy conservation and nonnegative of operator is discussed Furthermore, some construction methods of complete square-conservation difference schemes are introduced, including implicit and explicit complete square-conservation difference schemes, high time-accuracy and high-order compact complete square-conservation difference schemes At the same time, several computing examples are presented to show the computational effects of these schemes At last, this paper is summarized and a few important problems which need further research are proposed

关 键 词： 气候数值模拟 环境数值模拟 计算紊乱 非线性计算不稳定 完全平方守恒 紧致差分格式

领　　域： [理学] [理学] [理学] [理学]