Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 389, Issue -, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2021.114384
Keywords
Porous media flow; Biot consolidation; Total pressure; Transmission problem; Mixed finite element methods; Eye fluid poromechanics
Funding
- Monash Mathematics Research Fund [S05802-3951284]
- Ministry of Science and Higher Education of the Russian Federation [075-15-2020-926]
- American College of Veterinary Ophthalmologists Vision for Animals Foundation
- NSF [DMS 1818775, DMS 2111129]
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In this study, a new mixed-primal finite element scheme was proposed to solve the multiphysics model involving fluid flow and consolidation equations without the need for Lagrange multipliers. The research focused on numerical simulations related to geophysical flows and eye poromechanics, exploring different interfacial flow regimes that could help understand early morphologic changes associated with glaucoma in canine species.
We consider a multiphysics model for the flow of Newtonian fluid coupled with Biot consolidation equations through an interface, and incorporating total pressure as an unknown in the poroelastic region. A new mixed-primal finite element scheme is proposed solving for the pairs fluid velocity-pressure and displacement-total poroelastic pressure using Stokes-stable elements, and where the formulation does not require Lagrange multipliers to set up the usual transmission conditions on the interface. The stability and well-posedness of the continuous and semi-discrete problems are analysed in detail. Our numerical study is framed in the context of applicative problems pertaining to heterogeneous geophysical flows and to eye poromechanics. For the latter, we investigate different interfacial flow regimes in Cartesian and axisymmetric coordinates that could eventually help describe early morphologic changes associated with glaucoma development in canine species. (c) 2021 Elsevier B.V. All rights reserved.
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