A convergence study of monolithic simulations of flow and deformation in fractured poroelastic media

摘要

A consistent linearisation has been carried out for a monolithic solution procedure of a poroelastic medium with fluid-transporting fractures, including a comprehensive assessment of the convergence behaviour. The fracture has been modelled using a subgrid scale model with a continuous pressure across the fracture. The contributions to the tangential stiffness matrix of the fracture have been investigated to assess their impact on convergence. Simulations have been carried out for different interpolation orders and for Non-Uniform Rational B-Splines as interpolants vs Lagrangian polynomials. To increase the generality of the results, Newtonian as well as non-Newtonian (power-law) fluids have been considered. Unsurprisingly, a consistent linearisation invariably yields a quadratic convergence but comes at the expense of a loss of symmetry and recalculation of the contribution of the interface to the stiffness matrix at each iteration. When using a linear line search, however, the inclusion of only those terms of the interface stiffness that result in a symmetric and constant tangential stiffness matrix is sufficient to obtain a stable and convergent iterative process.