Multiscale finite-element method for linear elastic geomechanics

详细信息    查看全文

• 作者：Nicola Castelletto^a ; ^{ncastell@stanford.edu} ; Hadi Hajibeygi^b ; ^{h.hajibeygi@tudelft.nl} ; Hamdi A. Tchelepi^a ; ^{tchelepi@stanford.edu}
• 关键词：Multiscale methods ; Multiscale finite-element method ; Geomechanics ; Preconditioning ; Porous media
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：331
• 期：Complete
• 页码：337-356
• 全文大小：2073 K
• 卷排序：331

文摘

The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.