Comparing global and local implementations of nonlinear complementary problems for the modeling of multi-component two-phase flow with phase change phenomena

Compositional multiphase flow is considered to be one of the fundamental physical processes in the field of water resources research. The strong nonlinearity and discontinuity emerging from phase transition phenomena pose a serious challenge for numerical modeling. Recently, Lauser et al. (Adv Water Resour 34(8):957–966, 2011) have proposed a numerical scheme, namely the nonlinear complementary problem (NCP), to handle this strong nonlinearity. In this work, the NCP is implemented at both local and global levels of a finite element algorithm. In the former case, the NCP is integrated into the local thermodynamic equilibrium calculation, while in the latter one, it is formulated as one of the governing equations. The two different formulations have been investigated through three well-established benchmarks and analyzed for their efficiency and robustness. It is found that both globally and locally implemented NCP formulations are numerically more efficient and robust in comparison with traditional primary variable switching approach. In homogeneous media, the globally implemented NCP formulation leads to an approximately 20% faster simulation compared to the local NCP. This is because a nested Newton iteration for the local phase state identification can be avoided, and thus, the overall computational resources are saved accordingly. However, for problems involving strongly heterogeneous media, the locally integrated NCP formulation suppresses numerical oscillations and delivers more accurate and robust results, especially at the phase boundary.