Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix–fracture interfaces

IF 2.2 2区 数学 Q1 MATHEMATICS, APPLIED
Francesco Bonaldi, Jérôme Droniou, Roland Masson
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引用次数: 0

Abstract

We present a complete numerical analysis for a general discretization of a coupled flow–mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix–fracture interfaces, as well as nonlinear poromechanical coupling. Fractures are described as planar surfaces, yielding the so-called mixed- or hybrid-dimensional models. Small displacements and a linear elastic behavior are considered for the matrix. The model accounts for discontinuous fluid pressures at matrix–fracture interfaces in order to cover a wide range of normal fracture conductivities.

The numerical analysis is carried out in the Gradient Discretization framework (see J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin [The gradient discretisation method, Springer, Cham, 2018]), encompassing a large family of conforming and nonconforming discretizations. The convergence result also yields, as a by-product, the existence of a weak solution to the continuous model. A numerical experiment in 2D is presented to support the obtained result, employing a Hybrid Finite Volume scheme for the flow and second-order finite elements ( P 2 \mathbb {P}_2 ) for the mechanical displacement coupled with face-wise constant ( P 0 \mathbb P_0 ) Lagrange multipliers on fractures, representing normal stresses, to discretize the contact conditions.

基体-断裂界面无摩擦接触混合维度孔力学模型的数值分析
我们对断裂多孔介质中流动-力学耦合模型的一般离散化进行了完整的数值分析,考虑了单相流,包括基体-断裂界面的无摩擦接触以及非线性孔力学耦合。断裂被描述为平面,产生了所谓的混合维或混合维模型。基体考虑了小位移和线性弹性行为。该模型考虑了基体-断裂界面上不连续的流体压力,以涵盖广泛的法向断裂传导性。数值分析是在梯度离散化框架下进行的(见 J. Droniou、R. Eymard、T. Gallouët、C. Guichard 和 R. Herbin [The gradient discretisation method, Springer, Cham, 2018]),包含了一大系列符合和不符合离散化。作为副产品,收敛结果还得出了连续模型弱解的存在。为支持所获得的结果,介绍了二维数值实验,采用混合有限体积方案(Hybrid Finite Volume scheme)来计算流动,采用二阶有限元(P 2 \mathbb {P}_2 )来计算机械位移,并在裂缝上使用面常数(P 0 \mathbb P_0 )拉格朗日乘法器(代表法向应力)来离散接触条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematics of Computation
Mathematics of Computation 数学-应用数学
CiteScore
3.90
自引率
5.00%
发文量
55
审稿时长
7.0 months
期刊介绍: All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.
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