We present a high-order hybridizable discontinuous Galerkin method for the numerical solution of time-dependent three-phase flow in heterogeneous porous media. The underlying algorithm is a semi-implicit operator splitting approach that relaxes the nonlinearity present in the governing equations. By treating the subsequent equations implicitly, we obtain solution that remain stable for large time steps. The hybridizable discontinuous Galerkin method allows for static condensation, which significantly reduces the total number of degrees of freedom, especially when compared to classical discontinuous Galerkin methods. Several numerical tests are given, for example, we verify analytic convergence rates for the method, as well as examine its robustness in both homogeneous and heterogeneous porous media.

翻译：本文提出了一种高阶可杂交间断伽辽金方法，用于数值求解非均质多孔介质中的瞬态三相流问题。所采用的基本算法是一种半隐式算子分裂方法，能够有效缓解控制方程中存在的非线性。通过对后续方程进行隐式处理，我们获得了在大时间步长下仍保持稳定的解。可杂交间断伽辽金方法允许进行静态凝聚，与经典间断伽辽金方法相比，显著减少了总自由度数目。文中给出了若干数值算例，例如验证了该方法的理论收敛速率，并考察了其在均质与非均质多孔介质中的鲁棒性。