Implicit Hybrid Upwinding for two-phase flow in heterogeneous porous media with buoyancy and capillarity

We extend our previous results (Hamon et al., 2016 [18]) by generalizing the scheme to fully implicit coupled flow and transport to address realistic problems in multiple dimensions. The generalized scheme is supported by an analysis of its mathematical properties. Our multidimensional numerical examples, which range from buoyancy-driven flow with capillary barriers to viscous-dominated flow, demonstrate that the Implicit Hybrid Upwinding scheme improves the accuracy compared to the standard phase-based upwinding scheme, while leading to significant reductions in the number of nonlinear iterations in multiple dimensions.