Hybrid Finite Volume Discretization of Linear Elasticity Models on General Meshes
Hybrid Finite Volume Discretization of Linear Elasticity Models on General Meshes
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一般网格上线性弹性模型的混合有限体积离散化
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. Masson
中科院分区：
文献类型：
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作者：
D. A. Pietro;R. Eymard;S. Lemaire;R. Masson
本文提出了一种新的线弹性模型离散化方案，每个面只有一个自由度，对应于位移的法向分量。该格式基于分段常梯度结构和位移场的离散变分格式。用二阶线性插值法消除了位移场的切向分量。我们的主要动机是地质力学模型和油藏或二氧化碳储存模拟中产生的多孔介质流动的耦合。我们的方案通过构造保证了位移离散与Darcy流动模型中通常的以网格为中心的有限体积离散之间的相容条件。此外，它还适用于可能不协调的一般网格，如油藏和二氧化碳储存模拟中常用的角点几何。
This paper presents a new discretization scheme for linear elasticity models using only one degree of freedom per face corresponding to the normal component of the displacement. The scheme is based on a piecewise constant gradient construction and a discrete variational formulation for the displacement field. The tangential components of the displacement field are eliminated using a second order linear interpolation. Our main motivation is the coupling of geomechanical models and porous media flows arising in reservoir or CO2 storage simulations. Our scheme guarantees by construction the compatibility condition between the displacement discretization and the usual cell centered finite volume discretization of the Darcy flow model. In addition it applies on general meshes possibly non conforming such as Corner Point Geometries commonly used in reservoir and CO2 storage simulations.