Phase Space Volume Conservation under Space and Time Discretization Schemes for the Shallow-Water Equations
Phase Space Volume Conservation under Space and Time Discretization Schemes for the Shallow-Water Equations
复制标题
浅水方程时空离散格式下的相空间体积守恒
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
S. Reich
中科院分区：
文献类型：
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作者：
M. Sommer;S. Reich
将分析力学的概念应用于地球物理流动的数值离散技术是最近提出的。到目前为止，主要是能量和涡量守恒定律的作用进行了讨论，但最近相空间体积守恒也得到了解决。这个主题直接涉及统计流体力学和集合天气和气候预报的问题。在这里，相空间体积行为的不同的空间和时间离散方案的浅水方程的球进行了研究。空间对称和常见的时间离散的组合进行了比较。此外，时间可逆性和长期的量的平均值之间的关系进行了处理。
Abstract Applying concepts of analytical mechanics to numerical discretization techniques for geophysical flows has recently been proposed. So far, mostly the role of the conservation laws for energy- and vorticity-based quantities has been discussed, but recently the conservation of phase space volume has also been addressed. This topic relates directly to questions in statistical fluid mechanics and in ensemble weather and climate forecasting. Here, phase space volume behavior of different spatial and temporal discretization schemes for the shallow-water equations on the sphere are investigated. Combinations of spatially symmetric and common temporal discretizations are compared. Furthermore, the relation between time reversibility and long-time volume averages is addressed.