Numerical model reduction is exploited for computational homogenization of the model problem of a poroelastic medium under transient conditions. It is assumed that the displacement and pore pressure fields possess macro-scale and sub-scale (fluctuation) parts. A linearly independent reduced basis is constructed for the sub-scale pressure field using POD. The corresponding reduced basis for the displacement field is constructed in the spirit of the NTFA strategy. Evolution equations that define an apparent poro-viscoelastic macro-scale model are obtained from the continuity equation pertinent to the RVE. The present model represents an extension of models available in literature in the sense that the pressure gradient is allowed to have a non-zero macro-scale component in the nested $$\hbox {FE}^2$$ FE 2 setting. The numerical results show excellent agreement between the results from numerical model reduction and direct numerical simulation. It was also shown that even 3D RVEs give tractable solution times for full-fledged $$\hbox {FE}^2$$ FE 2 computations.

中文翻译：

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由均质化和数值模型简化​​获得的细尺度多孔弹性的多孔粘弹性替代模型

数值模型简化​​用于瞬态条件下多孔弹性介质模型问题的计算均质化。假设位移场和孔隙压力场具有宏观尺度和亚尺度（波动）部分。使用 POD 为子尺度压力场构建了一个线性独立的缩减基。位移场的相应缩减基是按照 NTFA 策略的精神构建的。定义一个明显的多孔粘弹性宏观模型的演化方程是从与 RVE 相关的连续性方程中获得的。本模型代表了文献中可用模型的扩展，因为在嵌套的 $$\hbox {FE}^2$$ FE 2 设置中允许压力梯度具有非零宏观分量。数值结果表明，数值模型简化​​和直接数值模拟的结果非常吻合。还表明，即使是 3D RVE 也为成熟的 $$\hbox {FE}^2$$ FE 2 计算提供了易于处理的求解时间。