Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous Media

We illustrate the advantages and disadvantages among two- and three-field formulations that are used to mimic the flow and solid deformation in heterogeneous porous media. Local mass conservation, flux approximation, average permeability alteration at each time step, and degrees of freedom (DOF) are utilized to evaluate each method. Our result presents that four out of six methods provide the local mass conservative while three out of those four methods produce approximately the same flux approximation and permeability alteration. Three-field formulation methods generally require a smaller time step to converge for solving the system of nonlinear equations. Besides, they have more DOF than that of the two-field formulation because they have one more primary variable, i.e. fluid velocity. The two-field formulation that is a combination of continuous and enriched Galerkin function space enjoys all the benefits while requires the least DOF among the methods that preserve local mass conservation property.