Numerical Models for Frictional Contact Mechanics and Flow in Fractured Porous Media: Discretization, Solvers and Applications

Massimiliano Ferronato, Univ. of Padova, Numerical Analysis
June 27, 2024 3:00 pm LSK 306

The simultaneous simulation of frictional contact mechanics and fluid flow in fractured geological media comprises tightly coupled physical processes and is a key component in the design of sustainable technologies for several subsurface applications, such as geothermal energy production, CO2 sequestration, and underground gas storage. Typically, the aperture and slippage between the contact surfaces drive the fluid flow in the fractures, while the pressure variation perturbs the stress state in the surrounding medium and influences the contact mechanics itself. This usually produces a stiff non-linear problem associated with a series of generalized saddle-point linear systems, whose solution is often hard to obtain efficiently.

In this work, we focus on a blended finite element/finite volume method, where the porous medium is discretized by low-order continuous finite elements with nodal unknowns; cell-centered Lagrange multipliers with a stabilization are used to prescribe the contact constraints; and the fluid flow in the fractures is described by a classical two-point flux approximation scheme. A class of scalable preconditioning strategies based on the physically informed block partitioning of the unknowns and state-of-the-art multigrid techniques is developed for the robust and efficient solution to the resulting sequence of linear systems with the Jacobian matrix. A set of numerical results concerning fractured porous media applications illustrate the robustness of the proposed approach, its algorithmic scalability, and the computational performance on large-size realistic problems.

Refreshments will be served preceding the talk, starting at 2:45.