Abstract We consider acoustic waves in fluid-saturated periodic media with large contrasts in the permeability and other poroelastic coefficients, whereby some of the mesoscopic material parameters depend on the scale parameter. The effective behaviour is described by a model obtained using the homogenization of the heterogeneous Biot continuum relevant to the mesoscopic level at which the dual porosity is featured by low permeability, whereas the primary porosity is very compliant. All material coefficients of the homogenized model depend on the frequency of incident waves. The macroscopic fields can be employed to reconstruct solutions at the mesoscopic level relevant to the heterogeneities. To validate the model, we consider heterogeneous strips with a finite scale lattice defining the heterogeneity. For such structures, the recovered mesoscopic response computed using the numerical homogenization method is compared with direct numerical simulations for various contrasts. For media featured by large contrast the double porosity model provides much better estimates of the wavelengths and other dispersion properties than the standard single porosity homogenized model. Moreover, the performed tests show computational efficiency of the two-scale simulations using the homogenized model, while the direct simulations of a heterogeneous medium become unfeasible because of requirements on the finite element discretization.

中文翻译：

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双孔Biot介质中波的数值模拟

摘要 我们考虑了流体饱和周期介质中的声波，其渗透率和其他多孔弹性系数有很大的差异，其中一些细观材料参数取决于尺度参数。有效行为由一个模型描述，该模型使用与双孔隙度具有低渗透性特征的细观水平相关的非均质 Biot 连续体的均质化，而初级孔隙度非常柔顺。均质模型的所有材料系数都取决于入射波的频率。宏观场可用于在与异质性相关的介观水平上重建解决方案。为了验证模型，我们考虑具有定义异质性的有限尺度晶格的异质条带。对于这样的结构，使用数值均匀化方法计算的恢复细观响应与各种对比的直接数值模拟进行比较。对于具有大对比度的介质，双孔隙率模型比标准的单孔隙率均质模型提供了更好的波长和其他色散特性估计。此外，所执行的测试显示了使用均质模型进行两尺度模拟的计算效率，而由于对有限元离散化的要求，对非均质介质的直接模拟变得不可行。对于具有大对比度的介质，双孔隙率模型比标准的单孔隙率均质模型提供了更好的波长和其他色散特性估计。此外，所执行的测试显示了使用均质模型进行两尺度模拟的计算效率，而由于对有限元离散化的要求，对非均质介质的直接模拟变得不可行。对于具有大对比度的介质，双孔隙率模型比标准的单孔隙率均质模型提供了更好的波长和其他色散特性估计。此外，所执行的测试显示了使用均质模型进行两尺度模拟的计算效率，而由于对有限元离散化的要求，对非均质介质的直接模拟变得不可行。