Constrained energy minimization based upscaling for coupled flow and mechanics

JOURNAL OF COMPUTATIONAL PHYSICS

卷:376

Article

Vasilyeva, Maria^1,2  Chung, Eric T.³  Efendiev, Yalchin^4,5  Kim, Jihoon⁶ 

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

[2] North Eastern Fed Univ, Dept Computat Technol, Yakutsk 677980, Russia

[3] CUHK, Dept Math, Hong Kong, Hong Kong, Peoples R China

[4] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[5] Texas A&M Univ, ISC, College Stn, TX 77843 USA

[6] Texas A&M Univ, Harold Vance Dept Petr Engn, College Stn, TX 77843 USA

关键词: Poroelasticity;    Embedded fracture model;    Multiscale methods;    Non-local multicontinuum method;    Constrained energy minimization;    Upscaling;   

DOI  :  10.1016/j.jcp.2018.09.054

来源: Elsevier

【 摘 要 】

In this paper, our aim is to present (1) an embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and (2) an upscaled model for the resulting fine grid equations. The mathematical model is described by the coupled system of equation for displacement, fracture and matrix pressures. For a fine grid approximation, we use the finite volume method for flow problem and finite element method for mechanics. Due to the complexity of fractures, solutions have a variety of scales, and fine grid approximation results in a large discrete system. Our second focus in the construction of the upscaled coarse grid poroelasticity model for fractured media. Our upscaled approach is based on the nonlocal multicontinuum (NLMC) upscaling for coupled flow and mechanics problem, which involves computations of local basis functions via an energy minimization principle. This concept allows a systematic upscaling for processes in the fractured porous media, and provides an effective coarse scale model whose degrees of freedoms have physical meaning. We obtain a fast and accurate solver for the poroelasticity problem on a coarse grid and, at the same time, derive a novel upscaled model. We present numerical results for the two dimensional model problem. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free