The proposed numerical scheme solves the linear poroelasticity equations, which refers to fluid flow within a deformable porous media under the assumption of relative small deformations. More precisely, we approximate the displacement of solid structure, the wetting phase pressure, and saturation of immiscible two-phase fluid flow in the deformable porous media in three dimensions. The model of linear poroelasticity is becoming increasingly essential in a diverse range of engineering fields such as the reservoir, biomedical, and environmental engineering. Thus predicting the deformation of the solid structure and the evolution of the phases in space and time plays an essential role in the risk-managing and decision-making process.

The proposed scheme solves the coupled equations sequentially while keeping each equation implicitly with respect to its unknown. A high-order interior penalty discontinuous Galerkin spatial discretization is combined with a backward Euler discretization in time. With this sequential approach, the equations are fully decoupled, which reduces the computational cost significantly compared to the existing implicit approach. Numerical results show the convergence of the scheme with the expected rates.