A Generalized Multiscale Finite Element Method for poroelasticity problems I: Linear problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:294

Article

Brown, Donald L.¹  Vasilyeva, Maria^2,3 

[1] Univ Bonn, Inst Numer Simulat, D-53115 Bonn, Germany

[2] North Eastern Fed Univ, Inst Math & Informat, Yakutsk, Republic Of Sak, Russia

[3] Texas A&M Univ, Inst Sci Computat, College Stn, TX 77843 USA

关键词: Generalized multiscale finite element;    Geomechanics;    Poroelasticity;    Model reduction;   

DOI  :  10.1016/j.cam.2015.08.007

来源: Elsevier

【 摘 要 】

In this paper, we consider the numerical solution of poroelasticity problems that are of Blot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in heterogeneous media. The two primary issues being the multiscale nature of the media and the solutions of the fluid and mechanics variables traditionally developed with separate grids and methods. For the numerical solution we develop and implement a Generalized Multiscale Finite Element Method (GMsFEM) that solves problem on a coarse grid by constructing local multiscale basis functions. The procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block. Using a snapshot space and local spectral problems, we construct a basis of reduced dimension. Finally, after multiplying by a multiscale partitions of unity, the multiscale basis is constructed in the offline phase and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions. We implement this algorithm on two heterogeneous media and compute error between the multiscale solution with the fine-scale solutions. Randomized oversampling and forcing strategies are also tested. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free