Coupled hydro-mechanical processes in variably saturated porous media can be encountered in several applications in geosciences and soil mechanics. They are ruled by highly nonlinear and strongly coupled equations of fluid flow in unsaturated porous media and quasi-static mechanical deformation. In this work, we develop an efficient and robust numerical scheme for unsaturated poroelasticity that allows for balancing computational requirements and accuracy. The spatial discretization is based on the Crouzeix-Raviart (CR) finite element method for both the displacement field and the hydraulic head. The CR method is locally mass conservative and uses low-order approximation, which alleviates the computational burden. The time discretization of the coupled nonlinear hydraulic mechanical equations is performed using high order time integration methods and efficient time stepping schemes via the method of lines (MOL).

中文翻译：

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用于可变饱和多孔介质中耦合流体力学过程的高效完全 Crouzeix-Raviart 有限元模型

在地球科学和土壤力学的多种应用中，可能会遇到可变饱和多孔介质中的耦合流体力学过程。它们由不饱和多孔介质中的流体流动和准静态机械变形的高度非线性和强耦合方程决定。在这项工作中，我们开发了一种有效且稳健的不饱和孔隙弹性数值方案，可以平衡计算要求和精度。位移场和水头的空间离散化基于 Crouzeix-Raviart (CR) 有限元方法。 CR方法是局部质量保守的并且使用低阶近似，这减轻了计算负担。耦合非线性液压机械方程的时间离散是通过直线法 (MOL) 使用高阶时间积分方法和有效的时间步进方案来执行的。