The linear and efficient structure-preserving method for the thermodynamical consistent model of two-phase flow in porous media with rock compressibility

In this paper, we first reformulate the thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media with rock compressibility and construct linear and efficient scheme based on the stabilized generalized scalar auxiliary variable (sGSAV) approach with the new relaxation in time and cell-centered finite difference (CCFD) method with upwind strategy in space. The constructed scheme is linear, only needs to solve one Poisson type equation and can be fully decoupled to solve the saturation and pressure at each time step. We rigorously prove that the constructed scheme is unconditionally energy stable, local mass conservative for each phase as well as pore volume, and bounds-preserving under appropriate conditions. In addition, we also construct a novel unconditionally bounds-preserving algorithm by using function transform approach based on the original model to better reflect the effect of global pressure. Finally, the reliability and efficiency of the proposed schemes can be verified through various numerical examples.