We present and analyze a discontinuous Galerkin method for the numerical modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We propose a high-order symmetric weighted interior penalty scheme that supports general polytopal grids and is robust with respect to strong heteorgeneities in the model coefficients. We focus on the treatment of the non-linear convective transport term in the energy conservation equation and we propose suitable stabilization techniques that make the scheme robust for advection-dominated regimes. The stability analysis of the problem and the convergence of the fixed-point linearization strategy are addressed theoretically under mild requirements on the problem's data. A complete set of numerical simulations is presented in order to assess the convergence and robustness properties of the proposed method.

翻译：针对全耦合非线性热-水-力问题的数值建模，我们提出并分析了一种间断伽辽金方法。该方法采用高阶对称加权内罚格式，支持一般多面体网格，并能在模型系数存在强非均质性时保持鲁棒性。我们重点处理了能量守恒方程中的非线性对流输运项，并提出了适当的稳定化技术，使得格式在对流主导区域具有鲁棒性。从理论上探讨了问题的稳定性分析及不动点线性化策略的收敛性，仅需对问题数据提出温和要求。通过完整的数值模拟系列，评估了所提方法的收敛性与鲁棒性。