An efficient preconditioner for mixed-dimensional contact poromechanics based on the fixed stress splitting scheme

TL;DR

This paper introduces a novel preconditioner for mixed-dimensional contact poromechanics simulations, improving efficiency and robustness by extending fixed stress schemes to complex coupled fracture and fluid problems.

Contribution

It develops a new preconditioner combining nested Schur complements and linear transformations to effectively decouple and solve strongly coupled poromechanics and contact mechanics problems.

Findings

Preconditioner improves convergence in coupled poromechanics simulations.

Method demonstrates scalability and robustness in numerical experiments.

Extends fixed stress schemes to matrix and fracture subdomains.

Abstract

Numerical simulation of fracture contact poromechanics is essential for various applications, including CO2 sequestration, geothermal energy production and underground gas storage. Modeling this problem accurately presents significant challenges due to the complex physics involved in strongly coupled poromechanics and frictional contact mechanics of fractures. The robustness and efficiency of the simulation heavily depends on a preconditioner for the linear solver, which addresses the Jacobian matrices arising from Newton's method in fully implicit time-stepping schemes. Developing an effective preconditioner is difficult because it must decouple three interdependent subproblems: momentum balance, fluid mass balance, and contact mechanics. The challenge is further compounded by the saddle-point structure of the contact mechanics problem, a result of the Augmented Lagrange formulation, which hinders the direct application of the well-established fixed stress approximation to decouple the poromechanics subproblem. In this work, we propose a preconditioner hat combines nested Schur complement approximations with a linear transformation, which addresses the singular nature of the contact mechanics subproblem. This approach extends the fixed stress scheme to both the matrix and fracture subdomains. We investigate analytically how the contact mechanics subproblem affects the convergence of the proposed fixed stress-based iterative scheme and demonstrate how it can be translated into a practical preconditioner. The scalability and robustness of the method are validated through a series of numerical experiments.