基质-裂缝界面处无摩擦接触的混合维度孔隙力学模型的数值分析
Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces
AI总结：
本文在梯度离散化框架下分析含无摩擦接触的混合维度孔隙力学模型，证明离散格式收敛并导出连续弱解存在性，且用二维混合有限体积与有限元实验验证。
摘要：
我们针对裂缝性多孔介质中耦合流动-力学模型的一般离散化，给出了一套完整的数值分析；该模型考虑单相流动，并包含基质-裂缝界面处的无摩擦接触以及非线性孔隙力学耦合。裂缝被描述为平面，从而形成所谓的混合维度或杂交维度模型。基质采用小位移和线弹性行为假设。模型允许基质-裂缝界面处的流体压力不连续，以覆盖广泛的裂缝法向传导率范围。数值分析在 Gradient Discretization（梯度离散化）框架内进行，该框架涵盖一大类协调与非协调离散化方法。收敛结果还作为副产品给出了连续模型弱解的存在性。文中给出了一个二维数值实验以支持所得结果；该实验在流动方面采用 Hybrid Finite Volume（混合有限体积）格式，在力学位移方面采用二阶有限元（P₂），并在裂缝上耦合面常值（P₀）Lagrange 乘子（表示法向应力），以离散接触条件。
英文摘要：
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, 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 ($\mathbb P_2$) for the mechanical displacement coupled with face-wise constant ($\mathbb P_0$) Lagrange multipliers on fractures, representing normal stresses, to discretize the contact conditions.
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