The Biot–Stokes coupling using total pressure: Formulation, analysis and application to interfacial flow in the eye

Ricardo Ruiz-Baier; Matteo Taffetani; Hans D. Westermeyer; Ivan Yotov

doi:10.1016/j.cma.2021.114384

The Biot–Stokes coupling using total pressure: Formulation, analysis and application to interfacial flow in the eye

Ricardo Ruiz-Baier^*, Matteo Taffetani, Hans D. Westermeyer, Ivan Yotov

^*Corresponding author for this work

Department of Engineering Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

18 Citations (Scopus)

Abstract

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.

Original language	English
Article number	114384
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	389
DOIs	https://doi.org/10.1016/j.cma.2021.114384
Publication status	Published - 1 Feb 2022

Bibliographical note

Funding Information:
RRB has been partially supported by the Monash Mathematics Research Fund S05802-3951284 and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers “Digital biodesign and personalised healthcare” No. 075-15-2020-926 ; MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM) ; HDW has been supported by a grant from the American College of Veterinary Ophthalmologists Vision for Animals Foundation VAFGL2017 ; and IY has received support from NSF grants DMS 1818775 and DMS 2111129 . In addition, the authors gratefully acknowledge the many fruitful discussions with Wietse Boon, Elfriede Friedmann, Miroslav Kuchta, Kent-André Mardal, and Sarah L. Waters, regarding models and suitable discretisations for interfacial flow couplings.

Funding Information:
RRB has been partially supported by the Monash Mathematics Research FundS05802-3951284 and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers ?Digital biodesign and personalised healthcare? No. 075-15-2020-926; MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM); HDW has been supported by a grant from the American College of Veterinary Ophthalmologists Vision for Animals FoundationVAFGL2017; and IY has received support from NSF grants DMS 1818775 and DMS 2111129. In addition, the authors gratefully acknowledge the many fruitful discussions with Wietse Boon, Elfriede Friedmann, Miroslav Kuchta, Kent-Andr? Mardal, and Sarah L. Waters, regarding models and suitable discretisations for interfacial flow couplings.

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Biot consolidation
Eye fluid poromechanics
Mixed finite element methods
Porous media flow
Total pressure
Transmission problem

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title = "The Biot–Stokes coupling using total pressure: Formulation, analysis and application to interfacial flow in the eye",

abstract = "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.",

keywords = "Biot consolidation, Eye fluid poromechanics, Mixed finite element methods, Porous media flow, Total pressure, Transmission problem",

author = "Ricardo Ruiz-Baier and Matteo Taffetani and Westermeyer, {Hans D.} and Ivan Yotov",

note = "Funding Information: RRB has been partially supported by the Monash Mathematics Research Fund S05802-3951284 and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers “Digital biodesign and personalised healthcare” No. 075-15-2020-926 ; MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM) ; HDW has been supported by a grant from the American College of Veterinary Ophthalmologists Vision for Animals Foundation VAFGL2017 ; and IY has received support from NSF grants DMS 1818775 and DMS 2111129 . In addition, the authors gratefully acknowledge the many fruitful discussions with Wietse Boon, Elfriede Friedmann, Miroslav Kuchta, Kent-Andr{\'e} Mardal, and Sarah L. Waters, regarding models and suitable discretisations for interfacial flow couplings. Funding Information: RRB has been partially supported by the Monash Mathematics Research FundS05802-3951284 and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers ?Digital biodesign and personalised healthcare? No. 075-15-2020-926; MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM); HDW has been supported by a grant from the American College of Veterinary Ophthalmologists Vision for Animals FoundationVAFGL2017; and IY has received support from NSF grants DMS 1818775 and DMS 2111129. In addition, the authors gratefully acknowledge the many fruitful discussions with Wietse Boon, Elfriede Friedmann, Miroslav Kuchta, Kent-Andr? Mardal, and Sarah L. Waters, regarding models and suitable discretisations for interfacial flow couplings. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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AU - Ruiz-Baier, Ricardo

AU - Taffetani, Matteo

AU - Westermeyer, Hans D.

AU - Yotov, Ivan

N1 - Funding Information: RRB has been partially supported by the Monash Mathematics Research Fund S05802-3951284 and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers “Digital biodesign and personalised healthcare” No. 075-15-2020-926 ; MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM) ; HDW has been supported by a grant from the American College of Veterinary Ophthalmologists Vision for Animals Foundation VAFGL2017 ; and IY has received support from NSF grants DMS 1818775 and DMS 2111129 . In addition, the authors gratefully acknowledge the many fruitful discussions with Wietse Boon, Elfriede Friedmann, Miroslav Kuchta, Kent-André Mardal, and Sarah L. Waters, regarding models and suitable discretisations for interfacial flow couplings. Funding Information: RRB has been partially supported by the Monash Mathematics Research FundS05802-3951284 and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers ?Digital biodesign and personalised healthcare? No. 075-15-2020-926; MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM); HDW has been supported by a grant from the American College of Veterinary Ophthalmologists Vision for Animals FoundationVAFGL2017; and IY has received support from NSF grants DMS 1818775 and DMS 2111129. In addition, the authors gratefully acknowledge the many fruitful discussions with Wietse Boon, Elfriede Friedmann, Miroslav Kuchta, Kent-Andr? Mardal, and Sarah L. Waters, regarding models and suitable discretisations for interfacial flow couplings. Publisher Copyright: © 2021 Elsevier B.V.

PY - 2022/2/1

Y1 - 2022/2/1

N2 - 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.

AB - 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.

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KW - Eye fluid poromechanics

KW - Mixed finite element methods

KW - Porous media flow

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KW - Transmission problem

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DO - 10.1016/j.cma.2021.114384

M3 - Article (Academic Journal)

AN - SCOPUS:85120977901

SN - 0045-7825

VL - 389

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 114384

ER -

The Biot–Stokes coupling using total pressure: Formulation, analysis and application to interfacial flow in the eye

Abstract

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Keywords

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