A scalable preconditioning framework for stabilized contact mechanics with hydraulically active fractures

TL;DR

This paper introduces a scalable preconditioning framework for efficiently solving coupled contact mechanics and fluid flow problems in fractured porous media, utilizing block partitioning and multigrid methods.

Contribution

It develops a novel preconditioning strategy for the coupled 3x3 block Jacobian system, enabling scalable and efficient solutions for complex fracture-fluid interaction problems.

Findings

The proposed preconditioning strategies demonstrate good scalability.

The methods effectively handle the coupling between mechanics and fluid flow.

Numerical results show strong performance on real-world fracture problems.

Abstract

A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered Lagrange multipliers and pressure unknowns used to impose the constraints and solve the fluid flow in the fractures, respectively. This formulation does not require any interpolation between different fields, but is not uniformly inf-sup stable and requires a stabilization. For the resulting 3 x 3 block Jacobian matrix, we design scalable preconditioning strategies, based on the physically-informed block partitioning of the unknowns and state-of-the-art multigrid preconditioners. The key idea is to restrict the system to a single-physics problem, approximately solve it by an inner algebraic multigrid approach, and finally prolong it back to the fully-coupled problem. Two different techniques are presented, analyzed and compared by changing the ordering of the restrictions. Numerical results illustrate the algorithmic scalability, the impact of the relative number of fracture-based unknowns, and the performance on a real-world problem.