AI 中文总结
研究裂缝多孔介质中耦合流动与力学问题，用扩展有限元法结合优化域分解策略求解，采用固定应力分裂方案和解耦子问题，证明固定应力方案与共轭梯度求解器组合对这类问题高效。
AI 中文摘要
本文提出一种数值方法来解决裂缝多孔介质中耦合流动与力学问题，该介质以混合维域表示。在这种公式中，三维网格元素可任意与裂缝相交。通过在三维网格上使用扩展有限元法（XFEM），位移在裂缝处不连续。力学问题被公式化为鞍点问题，用拉格朗日乘子强制裂缝处位移连续，所得拉格朗日乘子代表作用在裂缝表面的应力场。同样，压力场通过在非协调网格上的XFEM公式在裂缝处不连续，并使用专为混合维问题设计的基于优化的域分解策略计算。采用固定应力分裂方案解耦流动和力学子问题，在每个固定应力迭代中用共轭梯度（CG）法解决混合维压力问题。固定应力方案和CG求解器的组合对这类问题非常有效。
英文摘要
The present work proposes a numerical approach for solving coupled flow and mechanics problems in fractured porous media, represented as mixed-dimensional domains. In this formulation, the elements of the 3D mesh are allowed to arbitrarily intersect the fractures. Displacements are discontinuous across fractures through the use of the eXtended Finite Element Method (XFEM) on the 3D mesh. The mechanical problem is formulated as a saddle-point problem, in which Lagrange multipliers are used to enforce displacement continuity across the fractures. The resulting Lagrange multipliers represent the stress field acting on the fracture surfaces. Likewise, the pressure field is allowed to be discontinuous across fractures through the XFEM formulation on the non-conforming mesh and is computed using an optimization-based domain decomposition strategy specifically designed for mixed-dimensional problems. The fixed-stress splitting scheme is employed to decouple the flow and mechanics subproblems, while the mixed-dimensional pressure problem is solved at each fixed-stress iteration using the Conjugate Gradient (CG) method. The combination of the fixed-stress scheme and the CG solver proves to be highly effective for this class of problems.
