Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. This work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.

直接数值模拟（DNS）可以在孔尺度上产生最高的机械变形保真度预测，但是对于分析大量或大量样品而言，成本过高。离散元素方法（DEM）是一种有效的替代方法，但仅限于颗粒状介质，并且无法估计或控制预测误差。我们提出了一种孔级多尺度方法（PLMM），该方法可以有效地且可控制的精度近似于DNS。我们专注于具有任意微观结构，非均质矿物学，包含裂缝或缺陷的固结地质多孔介质的线性弹性响应。PLMM将固相分解为非重叠子域，在该子域上构造了本地基础函数。然后，这些基础与一个全局接口问题结合在一起，该问题解决了子域之间的滑动或粘滞接触情况。PLMM生成DNS的初始但准确的近似值，可以迭代地改进它。它适合并行性，并允许每个子域中使用不同的网格，模型和物理。还介绍了PLMM作为前置条件的代数解释，以允许在现有求解器中进行非侵入式实现。这项工作将PLMM在流体动力学方面的先前发展扩展到了固体力学，并使得将来可以扩展到对耦合的流动和力学问题进行建模。还介绍了PLMM作为前置条件的代数解释，以允许在现有求解器中进行非侵入式实现。这项工作将PLMM在流体动力学方面的先前发展扩展到了固体力学，并使得将来可以扩展到对耦合的流动和力学问题进行建模。还介绍了PLMM作为前置条件的代数解释，以允许在现有求解器中进行非侵入式实现。这项工作将PLMM在流体动力学方面的先前发展扩展到了固体力学，并使得将来可以扩展到对耦合的流动和力学问题进行建模。