A Novel Coupled bES-FEM Formulation with SUPG stabilization for Thermo-Hydro-Mechanical Analysis in Saturated Porous Media
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913384830599168 |
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| author | Tang, Zi-Qi Zhou, Xi-Wen Jin, Yin-Fu Yin, Zhen-Yu Zhang, Qi |
| author_facet | Tang, Zi-Qi Zhou, Xi-Wen Jin, Yin-Fu Yin, Zhen-Yu Zhang, Qi |
| contents | Two primary types of numerical instabilities often occur in low-order finite element method (FEM) analyses of thermo-hydro-mechanical (THM) phenomena: (1) pressure oscillations arising improper interpolation of pressure and displacement fields; and (2) spatial oscillations induced by nonlinear convection terms in convection-dominated scenarios. In response to these issues, this paper proposes a novel stabilized edge-based smoothed FEM with a bubble function (bES-FEM) for THM analysis within saturated porous media. In the proposed framework, a cubic bubble function is first incorporated into ES-FEM to efficiently mitigate pressure oscillations that breach the Inf-Sup condition, and then the Streamline Upwind Petrov-Galerkin (SUPG) scheme is adopted in bES-FEM to effectively reduce the spurious oscillations in convection-dominated heat transfer scenarios. The accuracy of the bES-FEM with SUPG formulation for THM coupled problems is validated through a series of five benchmark tests. Moreover, the simulations of open-loop ground source energy systems demonstrate the proposed method's exceptional capability in tackling complex THM challenges in real-world applications. All the obtained results showcase the superiority of proposed bES-FEM with SUPG in eliminating the spatial and pressure oscillations, marking it as a promising tool for the exploration of coupled THM issues. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_05138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Novel Coupled bES-FEM Formulation with SUPG stabilization for Thermo-Hydro-Mechanical Analysis in Saturated Porous Media Tang, Zi-Qi Zhou, Xi-Wen Jin, Yin-Fu Yin, Zhen-Yu Zhang, Qi Geophysics Numerical Analysis Two primary types of numerical instabilities often occur in low-order finite element method (FEM) analyses of thermo-hydro-mechanical (THM) phenomena: (1) pressure oscillations arising improper interpolation of pressure and displacement fields; and (2) spatial oscillations induced by nonlinear convection terms in convection-dominated scenarios. In response to these issues, this paper proposes a novel stabilized edge-based smoothed FEM with a bubble function (bES-FEM) for THM analysis within saturated porous media. In the proposed framework, a cubic bubble function is first incorporated into ES-FEM to efficiently mitigate pressure oscillations that breach the Inf-Sup condition, and then the Streamline Upwind Petrov-Galerkin (SUPG) scheme is adopted in bES-FEM to effectively reduce the spurious oscillations in convection-dominated heat transfer scenarios. The accuracy of the bES-FEM with SUPG formulation for THM coupled problems is validated through a series of five benchmark tests. Moreover, the simulations of open-loop ground source energy systems demonstrate the proposed method's exceptional capability in tackling complex THM challenges in real-world applications. All the obtained results showcase the superiority of proposed bES-FEM with SUPG in eliminating the spatial and pressure oscillations, marking it as a promising tool for the exploration of coupled THM issues. |
| title | A Novel Coupled bES-FEM Formulation with SUPG stabilization for Thermo-Hydro-Mechanical Analysis in Saturated Porous Media |
| topic | Geophysics Numerical Analysis |
| url | https://arxiv.org/abs/2406.05138 |