Generalized Multiscale Finite Element Method for thermoporoelasticity problems in heterogeneous and fractured media

Ammosov, Dmitry; Vasilyeva, Maria; Chung, Eric T.

doi:10.1016/j.cam.2021.113995

Cited by 6 publications

(3 citation statements)

References 34 publications

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“…The equilibrium equation for the displacement fields u i of heterogeneous porous media (PM) is expressed as. 31,35,38…”

Section: Nomenclaturementioning

confidence: 99%

“…All these mesoscopic cell functions are further expanded to the microscopic levels. Then, we substitute the meso-micro high-order expansions of mesoscopic cell functions into Equations ( 37) and (38) to obtain the three-scale high-order models for the HM coupling problems. This strategy can substantially reduce the computational costs of mesoscopic cell functions defined on the heterogeneous unit cell 𝛺 y .…”

Section: Physical Mechanisms and Algorithm Aspects For Three-scale Mo...mentioning

confidence: 99%

“…The equilibrium equation for the displacement fields

{u}_i

of heterogeneous porous media (PM) is expressed as 31,35,38

{\rho}_s\frac{\partial^2{u}_i}{\partial {t}^2}-\frac{\partial }{\partial {x}_j}\left({C}_{ij kl}\frac{\partial {u}_k}{\partial {x}_l}-{\alpha}_{ij}p\right)={f}_i(x),

here, the Einstein summation convention is employed, that is,

{a}_i{b}_i={a}_1{b}_1+{a}_2{b}_2+{a}_3{b}_3

.…”

Section: Dynamic Hydro‐mechanical Coupling Problems In Heterogeneous ...mentioning

confidence: 99%

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High‐order models for hydro‐mechanical coupling problems in multiscale porous media

Zuo,

Yang,

Cui

et al. 2024

Numerical Meth Engineering

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An accurate prediction of nonlinear hydro‐mechanical (HM) coupling in subsurface structures with pronounced heterogeneity at multiple spatial scales is still an open topic and crucial for numerous engineering applications, for example, hydraulic fracturing and enhanced geothermal systems. In this study, novel high‐order multi‐scale asymptotic solutions are developed to accurately capture the locally oscillating characteristics of gas flow and solid displacement fields at multiple scales. First, the formal macro‐meso two‐scale asymptotic expansion is performed to establish the homogenized solutions and macro‐meso high‐order models which can predict the HM coupling problems at the macroscale and mesoscale. By directly expanding the cell functions defined at the mesoscale to the microscopic levels, the high‐order two‐scale expansion for the mesoscopic cell functions is built, and the upscaled relations for the flow parameters and constitutive coefficients from the microscale to the mesoscale and macroscale are developed correspondingly. The multi‐scale low/high‐order models are established by combining the high‐order expansion of all cell functions at the mesoscale and the developed macro‐meso two‐scale models. The main contributions are that the present approaches follow the reverse thought processes of reiteration homogenization methods, and offer a very innovative and efficient way to establish high‐accuracy high‐order models for the nonlinear HM coupling problems in the heterogeneous porous medium with any number of spatial scales. The effectiveness and accuracy of the present solution are validated by several representative cases with different constitutive coefficient contrasts. The results demonstrate that the high‐order solutions provide an accurate prediction for gas transport and solid deformation of heterogeneous porous media with multi‐scale configurations.

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“…The equilibrium equation for the displacement fields u i of heterogeneous porous media (PM) is expressed as. 31,35,38…”

Section: Nomenclaturementioning

confidence: 99%

Section: Physical Mechanisms and Algorithm Aspects For Three-scale Mo...mentioning

confidence: 99%

“…The equilibrium equation for the displacement fields

{u}_i

of heterogeneous porous media (PM) is expressed as 31,35,38

{\rho}_s\frac{\partial^2{u}_i}{\partial {t}^2}-\frac{\partial }{\partial {x}_j}\left({C}_{ij kl}\frac{\partial {u}_k}{\partial {x}_l}-{\alpha}_{ij}p\right)={f}_i(x),

here, the Einstein summation convention is employed, that is,

{a}_i{b}_i={a}_1{b}_1+{a}_2{b}_2+{a}_3{b}_3

.…”

Section: Dynamic Hydro‐mechanical Coupling Problems In Heterogeneous ...mentioning

confidence: 99%

See 1 more Smart Citation

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

Zuo,

Yang,

Cui

et al. 2024

Numerical Meth Engineering

View full text Add to dashboard Cite

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Numerical simulation of language interactions using online coupled Generalized Multiscale Finite Element Method

Ammosov

Grigorev

Stepanov

et al. 2023

Journal of Computational and Applied Mathematics

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Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation

Ammosov

Grigorev

Stepanov

et al. 2023

Journal of Computational and Applied Mathematics

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Generalized Multiscale Finite Element Method for thermoporoelasticity problems in heterogeneous and fractured media

Cited by 6 publications

References 34 publications

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

Numerical simulation of language interactions using online coupled Generalized Multiscale Finite Element Method

Partial learning using partially explicit discretization for multicontinuum/multiscale problems. Fractured poroelastic media simulation

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