Abstract
We study a poromechanic problem in presence of a moving boundary. The poroelastic material is described by means of the Biot model while the moving boundary accounts for the effect of surface erosion of the material. We focus on the numerical approximation of the problem, in the framework of the finite element method. To avoid re-meshing along with the evolution of the boundary, we adopt the cut finite element approach. The main issue of this strategy consists of the ill-conditioning of the finite element matrices in presence of cut elements of small size. We show, by means of numerical experiments and theory, that this issue significantly decreases the performance of the numerical solver. For this reason, we propose a strategy that allows to overcome the illconditioned behavior of the discrete problem. The resulting solver is based on the fixed stress approach, used to iteratively decompose the Biot equations, combined with the ghost penalty stabilization and preconditioning applied to the pressure and displacement sub-problems respectively.
Highlights
Reconstructing the stress and deformation history of a sedimentary basin is a challenging and important problem in the geosciences [32]
We study a poromechanic problem in presence of a moving boundary
The resulting solver is based on the fixed stress approach, used to iteratively decompose the Biot equations, combined with the ghost penalty stabilization and preconditioning applied to the pressure and displacement sub-problems respectively
Summary
Reconstructing the stress and deformation history of a sedimentary basin is a challenging and important problem in the geosciences [32]. Since the scope of this work is more focused on the methodology, precisely the development of a numerical solver, we address a simplified problem configuration which features a slab of porous, deformable material that is homogeneous, completely saturated with water and affected by a prescribed mixed erosion deposition profile on the top surface. It is well known that this approach significantly worsens the conditioning of the discretized operators, because the finite element discretization is set on cut elements that may become arbitrarily small and skewed, according to the configuration of the unfitted boundary or interface with respect to the computational mesh To override this issue, several techniques have been proposed.
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