Algebraically stabilized Lagrange multiplier method for frictional contact mechanics with hydraulically active fractures

• Published in: Computer methods in applied mechanics and engineering 2020-08, Vol.368 (C), p.113161, Article 113161
• Main Authors: Franceschini, Andrea, Castelletto, Nicola, White, Joshua A., Tchelepi, Hamdi A.
• Format: Article
• Language: English
• Subjects: Benchmarks; Computational fluid dynamics; Computer simulation; Contact mechanics; Contact pressure; Darcy fracture flow; Deformation; ENGINEERING; Finite volume method; Fluid flow; Fluid pressure; Fractures; Interpolation; Lagrange multiplier; Lagrange multipliers; Mass balance; Mathematical models; Mechanics (physics); Robustness (mathematics); Stabilization; Three dimensional analysis
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113161

Accurate numerical simulation of coupled fracture/fault deformation and fluid flow is crucial to the performance and safety assessment of many subsurface systems. In this work, we consider the discretization and enforcement of contact conditions at such surfaces. The bulk rock deformation is simulated using low-order continuous finite elements, while frictional contact conditions are imposed by means of a Lagrange multiplier method. We employ a cell-centered finite-volume scheme to solve the fracture fluid mass balance equation. From a modeling perspective, a convenient choice is to use a single grid for both mechanical and flow processes, with piecewise-constant interpolation of Lagrange multipliers, i.e., contact tractions and fluid pressure. Unfortunately, this combination of displacement and multiplier variables is not uniformly inf–sup stable, and therefore requires a stabilization technique. Starting from a macroelement analysis, we develop two algebraic stabilization approaches and compare them in terms of robustness and convergence rate. The proposed approaches are validated against challenging analytical two- and three-dimensional benchmarks to demonstrate accuracy and robustness. These benchmarks include both pure contact mechanics problems and well as problems with tightly-coupled fracture flow. •A low order finite element/finite volume mixed formulation for the coupled simulation of contact mechanics and fluid flow in hydraulically active fractures is presented.•The discretization is convenient from an implementation point of view, but it is not intrinsically stable.•Three stabilization approaches are presented and compared.•In particular, a fully algebraic technique is developed and tested against several analytical benchmarks, showing excellent performance.