Novel Stabilizations for A Piecewise Constant Lagrangian Formulation of Frictional Contact Mechanics with Hydraulically Active Fractures

Summary Many reservoir engineering applications involve tight coupling between fluid flow processes and poromechanical deformation. In particular, accurate simulation of phenomena like fault reactivation and fracture propagation strongly depends on the two-way coupled fluid-structure interaction. In this work, we focus on modeling frictional contact mechanics coupled with hydraulically active fractures. Specifically, fluid flow occurs inside the fracture, with the fluid pressure acting as an external load for the continuous body, and the conductivity of the fracture is a strong function of the bulk rock deformation. In our numerical model we adopt a single conforming computational grid for both mechanical and flow processes. A cell-centered finite-volume scheme is used to solve the pressure field inside the fracture while the displacement field in the surrounding rock is approximated through first-order continuous finite elements. Contact conditions on the fracture are imposed through Lagrange multipliers, which represent the contact tractions. For the Lagrange multipliers we employ the same piecewise-constant interpolation (component-wise) used for the pressure approximation. While this approximation space is convenient from a modeling perspective, the combination of linear displacement and piecewise constant traction/pressure variables is not uniformly inf-sup stable and requires a suitable stabilization. Hence, starting from a macroelement analysis, we develop three novel techniques, one local and two global, which aim at stabilizing the traction jumps across the elements discretizing the fracture surface. Effectiveness and robustness of proposed stabilization strategies are demonstrated and compared against complex analytical two- and three-dimensional benchmarks from the literature.