Statistical mechanics of Arakawa's discretizations
Statistical mechanics of Arakawa's discretizations
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荒川离散化的统计力学
DOI：
10.1016/j.jcp.2007.09.002
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
J. Frank
中科院分区：
文献类型：
--
作者：
S. Dubinkina;J. Frank
地球物理流体模型长时间积分所得模拟数据的统计分析结果在很大程度上取决于所采用数值离散化的守恒性质。对于具有地形强迫的准地转流来说，这是一个很好的统计力学。统计力学理论是为由Arakawa引起的三次离散化引起的离散动力系统构建的[Arakawa，流体运动方程长期数值积分的计算设计：二维不可压缩流动]。第一部分：计算机。物理学报1(1966)119-143]，它能保存能量、熵或两者兼而有之。用保守时间积分器和投影时间积分器进行的数值实验表明，统计理论准确地解释了离散化后所观察到的统计差异。
The results of statistical analysis of simulation data obtained from long time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization used. This is illustrated for quasi-geostrophic flow with topographic forcing, for which a well established statistical mechanics exists. Statistical mechanical theories are constructed for the discrete dynamical systems arising from three discretizations due to Arakawa [Arakawa, Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comput. Phys. 1 (1966) 119–143] which conserve energy, enstrophy or both. Numerical experiments with conservative and projected time integrators show that the statistical theories accurately explain the differences observed in statistics derived from the discretizations.