In fully-implicit two-phase pore-network models, developing a well-converged scheme remains a major challenge, primarily due to the discontinuities in the phase conductivities. This paper addresses these numerical issues by proposing a generalized flux function that establishes a continuous flux expression for two-phase flows by introducing an additional throat variable $\Theta$. Two approaches for expressing this additional throat variable are introduced: the first applies regularization strategies, while the second constructs an additional residual constraint equation. It is shown that this approach significantly improves accuracy and ensures the temporal convergence, as demonstrated through various numerical examples.

翻译：在全隐式两相孔隙网络模型中，开发具有良好收敛性的方案仍然是一个主要挑战，这主要源于相传导率的不连续性。本文通过提出一种广义通量函数来解决这些数值问题，该函数通过引入附加喉道变量 $\Theta$ 为两相流动建立了连续的通量表达式。文中介绍了两种表达该附加喉道变量的方法：第一种采用正则化策略，第二种则构建附加的残差约束方程。数值算例表明，该方法显著提高了计算精度并确保了时间收敛性。