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首页> 外文期刊>Journal of Engineering Mechanics >Comparison of upscaling methods in poroelasticity and its generalizations
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Comparison of upscaling methods in poroelasticity and its generalizations

机译：多孔弹性放大方法的比较及其推广

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Four methods of upscaling coupled equations at the microscale to equations valid at the mesoscale and/or macroscale for fluid-saturated and partially saturated porous media will be discussed, compared, and contrasted. The four methods are: (1) effective medium theory, (2) mixture theory, (3) two-scale and multiscale homogenization, and (4) volume averaging. All these methods have advantages for some applications and disadvantages for others. For example, effective medium theory, mixture theory, and homogenization methods can all give formulas for coefficients in the up-scaled equations, whereas volume averaging methods give the form of the up-scaled equations but generally must be supplemented with physical arguments and/or data in order to determine the coefficients. Homogenization theory requires a great deal of mathematical insight from the user in order to choose appropriate scalings for use in the resulting power-law expansions, while volume averaging requires more physical insight to motivate the steps needed to find coefficients. Homogenization often is performed on periodic models, while volume averaging does not require any assumption of periodicity and can therefore be related very directly to laboratory and/or field measurements. Validity of the homogenization process is often limited to specific ranges of frequency-in order to justify the scaling hypotheses that must be made-and therefore cannot be used easily over wide ranges of frequency. However, volume averaging methods can quite easily be used for wide band data analysis. So, we learn from these comparisons that a researcher in the theory of poroelasticity and its generalizations needs to be conversant with two or more of these methods to solve problems generally.
机译：将讨论，比较和对比四种将微尺度耦合方程升阶为对流体饱和和部分饱和多孔介质的中尺度和/或宏观尺度有效的方程的方法。这四种方法是：（1）有效介质理论，（2）混合理论，（3）两尺度和多尺度均质化以及（4）体积平均。所有这些方法对于某些应用程序都有优点，而对于其他应用程序则有缺点。例如，有效的介质理论，混合理论和均质化方法都可以给出放大方程的系数公式，而体积平均法则可以给出放大方程的形式，但通常必须补充物理参数和/或数据以确定系数。均质化理论需要用户提供大量的数学知识，以便选择适当的缩放比例以用于产生的幂律扩展，而体积平均需要更多的物理知识来激发寻找系数所需的步骤。均质化通常在周期性模型上执行，而体积平均不需要任何周期性假设，因此可以非常直接地与实验室和/或现场测量相关。均质化过程的有效性通常限于特定的频率范围，以证明必须进行的缩放假设，因此无法在较宽的频率范围内轻松使用。但是，体积平均方法可以很容易地用于宽带数据分析。因此，我们从这些比较中获悉，多孔弹性理论及其推广的研究人员需要熟悉其中两种或更多种方法以普遍解决问题。

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