Numerical solvers for a poromechanic problem with a moving boundary
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 fin...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2019-01-01
|
| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2019.4.824/fulltext.html |
| _version_ | 1818218220172083200 |
|---|---|
| author | Daniele Cerroni Florin Adrian Radu Paolo Zunino |
| author_facet | Daniele Cerroni Florin Adrian Radu Paolo Zunino |
| author_sort | Daniele Cerroni |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T07:20:18Z |
| format | Article |
| id | doaj.art-08c25429e6a34536a808cf490a79e3cd |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-12T07:20:18Z |
| publishDate | 2019-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-08c25429e6a34536a808cf490a79e3cd2022-12-22T00:33:24ZengAIMS PressMathematics in Engineering2640-35012019-01-011482484810.3934/mine.2019.4.824Numerical solvers for a poromechanic problem with a moving boundaryDaniele Cerroni0 Florin Adrian Radu1Paolo Zunino21 MOX, Department of Mathematics, Politecnico di Milano, Italy2 PMG, Department of Mathematics, University of Bergen, Norway1 MOX, Department of Mathematics, Politecnico di Milano, ItalyWe 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.https://www.aimspress.com/article/10.3934/mine.2019.4.824/fulltext.htmlporomechanicsmoving boundaryfixed-stress approachcut finite elementspreconditioning |
| spellingShingle | Daniele Cerroni Florin Adrian Radu Paolo Zunino Numerical solvers for a poromechanic problem with a moving boundary Mathematics in Engineering poromechanics moving boundary fixed-stress approach cut finite elements preconditioning |
| title | Numerical solvers for a poromechanic problem with a moving boundary |
| title_full | Numerical solvers for a poromechanic problem with a moving boundary |
| title_fullStr | Numerical solvers for a poromechanic problem with a moving boundary |
| title_full_unstemmed | Numerical solvers for a poromechanic problem with a moving boundary |
| title_short | Numerical solvers for a poromechanic problem with a moving boundary |
| title_sort | numerical solvers for a poromechanic problem with a moving boundary |
| topic | poromechanics moving boundary fixed-stress approach cut finite elements preconditioning |
| url | https://www.aimspress.com/article/10.3934/mine.2019.4.824/fulltext.html |
| work_keys_str_mv | AT danielecerroni numericalsolversforaporomechanicproblemwithamovingboundary AT florinadrianradu numericalsolversforaporomechanicproblemwithamovingboundary AT paolozunino numericalsolversforaporomechanicproblemwithamovingboundary |