Link to the University of Pittsburgh Homepage
Link to the University Library System Homepage Link to the Contact Us Form

Mixed Formulations for Fluid-poroelastic Structure Interaction

Li, Tongtong (2021) Mixed Formulations for Fluid-poroelastic Structure Interaction. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

This is the latest version of this item.

Download (8MB) | Preview


This thesis focuses on the development of mixed finite element methods for the coupled problem arising in the interaction between free fluid flow and flow in a deformable poroelastic medium. We adopt the Stokes or the Navier-Stokes equations to model the free fluid region, and the Biot system to describe the poroelastic medium. On the interface, mass conservation, balance of stresses and the slip with friction conditions are imposed via the Lagrange multiplier method.
We first develop a new mixed elasticity formulation for the Stokes-Biot problem. We establish the existence and uniqueness of a solution for the continuous weak formulation and perform stability and error analyses for the semi-discrete continuous-in-time mixed finite element approximation. We present numerical experiments that verify the theoretical results and illustrate the robustness of the method with respect to the physical parameters.
We then extend the previous results for the Stokes-Biot problem by considering dual-mixed formulations in both the fluid and structure regions. Well-posedness and stabil- ity results are established for the continuous weak formulation, as well as a semi-discrete continuous-in-time formulation with non-matching grids. In addition, we develop a new multipoint stress-flux mixed finite element method by involving the vertex quadrature rule. Well-posedness and error analysis with corresponding rates of convergences for the fully- discrete scheme are complemented by several numerical experiments.
Next, we propose an augmented fully mixed formulation for the coupled quasi-static Navier-Stokes – Biot model by introducing a ”nonlinear-pseudostress” tensor linking the pseudostress tensor with the convective term in the Navier-Stokes equations and augment- ing the variational formulation with suitable Galerkin redundant terms. We show well- posedness, derive stability and error analysis results for the associated mixed finite element approximation and conduct several numerical experiments.
Finally, we derive a fully mixed formulation with weakly symmetric stresses for the Navier-Stokes – Biot model. We develop an extension of the multipoint stress-flux mixed finite element method that allows for local elimination of the fluid and poroelastic stresses, vorticity, and rotation, resulting in a positive definite finite volume scheme. A numerical convergence study is presented for the fully discrete scheme.


Social Networking:
Share |


Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Li, Tongtongtol24@pitt.edutol24
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairYotov,
Committee MemberCaucao,
Committee MemberTrenchea,
Committee MemberWang,
Date: 8 October 2021
Date Type: Publication
Defense Date: 9 July 2021
Approval Date: 8 October 2021
Submission Date: 12 July 2021
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 250
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: numerical analysis, mixed finite element methods, FPSI, Stokes-Biot model, Navier-Stokes -- Biot model, multipoint stress-flux, augmented formulation, finite volume method
Date Deposited: 08 Oct 2021 19:19
Last Modified: 08 Oct 2021 19:19

Available Versions of this Item

  • Mixed Formulations for Fluid-poroelastic Structure Interaction. (deposited 08 Oct 2021 19:19) [Currently Displayed]


Monthly Views for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item