热-孔隙弹性系统的混合化间断伽辽金方法
Hybridizable Discontinuous Galerkin Methods for Thermo-Poroelastic Systems
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中文总结 AI 辅助
本文提出一种高阶混合化间断伽辽金（HDG）方法求解线性热-孔隙弹性波传播问题，通过一阶双曲系统与能量一致离散保证守恒，并给出hp收敛分析及数值验证。
中文摘要 AI 辅助
我们针对完全动态的线性热-孔隙弹性问题提出了一种高阶混合化间断伽辽金（HDG）格式。控制方程被表述为一阶双曲系统，将固体速度、流体速度、热通量、有效应力、孔隙压力和温度作为状态变量。我们利用半群理论建立了连续问题的适定性，并发展了一种能量一致的HDG离散化。该方法利用了HDG的计算优势——包括局部性和静态凝聚——同时保持耦合系统的能量守恒。我们建立了$hp$收敛性分析，并通过全面的数值实验加以支持，证实了理论收敛阶，展示了该方法在非均匀介质中热-孔隙弹性波传播的有效性。
英文摘要
We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and fluid velocities, heat flux, effective stress, pore pressure, and temperature as state variables. We establish well-posedness of the continuous problem using semigroup theory and develop an energy-consistent HDG discretization. The method exploits computational advantages of HDG-including locality and static condensation-while maintaining energy conservation for the coupled system. We establish an $hp$-convergence analysis and support it with comprehensive numerical experiments, confirming the theoretical rates and showcasing the method's effectiveness for thermo-poroelastic wave propagation in heterogeneous media.
