The role of scaling laws in upscaling
The role of scaling laws in upscaling
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DOI：
10.1016/j.advwatres.2008.08.015
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发表时间：
2009-05
影响因子：
4.7
通讯作者：
B. Wood
中科院分区：
文献类型：
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作者：
B. Wood
在这项工作中，讨论了复杂地下水文系统的粗粒化过程，并特别努力研究了平均的数学过程与升尺度过程之间的区别。有可能表明，平均过程本身不足以减少描述复杂异质系统所需的自由度。自由度的减少完全是由随后的缩放定律完成的，人们认为这些缩放定律是消除系统中冗余（或低值）信息的有效过滤器。给出了随机非均质多孔介质中有效色散张量上尺度的具体例子。结果表明：(1)一般情况下，可以建立一个平均描述，但系统包含的信息不会比原问题少；(2)通过采用多个标度定律，可以得到与前面结果相同的时间和空间上的非局域表达式；(3)通过增加一个假设，可以得到局域宏观输运方程。
In this work the process of coarse-graining in complex subsurface hydrologic systems is discussed, with a particular effort made to examine the difference between the mathematical process of averaging as distinct from the process of upscaling. It is possible to show that the process of averaging itself is not sufficient to reduce the number of degrees of freedom required to describe a complex heterogeneous system. The reduction of the number of degrees of freedom is accomplished entirely by the subsequent scaling laws that one assumes are valid filters for eliminating redundant (or low value) information in the system. A specific example is given for the upscaling of the effective dispersion tensor in a randomly heterogeneous porous medium. It is shown that: (1) generally, an averaged description can be developed, but the system does not contain any less information than the original problem; (2) by adopting a number of scaling laws, a nonlocal in time and in space formulation can be obtained that is identical to results obtained previously, and (3) by making one additional assumption, a local macroscale transport equation can be obtained.