Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome this computational challenge, various multiscale methods are developed. In this paper, we consider a class of linear poroelasticity problems in high contrast heterogeneous porous media, and develop a mixed generalized multiscale finite element method (GMsFEM) to obtain a fast computational method. Our aim is to develop a multiscale method that is robust with respect to the heterogeneities and contrast of the media, and gives a mass conservative fluid velocity field. We will construct decoupled multiscale basis functions for the elastic displacement as well as fluid velocity. Our multiscale basis functions are local. The construction is based on some suitable choices of local snapshot spaces and local spectral decomposition, with the goal of extracting dominant modes of the solutions. For the pressure, we will use piecewise constant approximation. We will present several numerical examples to illustrate the performance of our method. Our results indicate that the proposed method is able to give accurate numerical solutions with a small degree of freedoms.

流体与固体之间相互作用的精确数值模拟在应用中起着重要作用。在实际情况下，这项任务具有挑战性，因为媒体通常是高度异构的，并且对比度非常大。为了克服这一计算难题，开发了各种多尺度方法。在本文中，我们考虑了高对比度非均质多孔介质中的一类线性孔隙弹性问题，并开发了一种混合广义多尺度有限元方法（GMsFEM），以获得一种快速的计算方法。我们的目标是开发一种多尺度方法，该方法在介质的非均质性和对比度方面具有鲁棒性，并给出了质量守恒的流体速度场。我们将为弹性位移以及流体速度构造解耦的多尺度基函数。我们的多尺度基础函数是局部的。建设是基于本地快照空间和局部谱分解的一些合适的选择，与提取解决方案的主导模式的目标。对于压力，我们将使用分段常数近似。我们将提供几个数值示例来说明我们方法的性能。我们的结果表明，所提出的方法能够以较小的自由度给出精确的数值解。