Hageman, T. and de Borst, R. orcid.org/0000-0002-3457-3574 (2020) A convergence study of monolithic simulations of flow and deformation in fractured poroelastic media. International Journal for Numerical Methods in Engineering, 121 (3). pp. 393-410. ISSN 0029-5981
Abstract
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 sub‐grid 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 which result in a symmetric and constant tangential stiffness matrix is sufficient to obtain a stable and convergent iterative process.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 John Wiley & Sons. This is an author-produced version of a paper subsequently published in International Journal for Numerical Methods in Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Poroelasticity; fracture; monolithic solvers; convergence; Newton-Raphson method |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number European Commission - Horizon 2020 664734 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 18 Sep 2019 08:23 |
Last Modified: | 16 Dec 2021 08:45 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/nme.6213 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:151008 |