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Modelling of flow and transport of non-Newtonian fluids interacting with poroelastic media

Nguyen, Truong (2019) Modelling of flow and transport of non-Newtonian fluids interacting with poroelastic media. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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We propose and analyze a model for solving the coupled problem arising in the interaction of a free fluid with a poroelastic structure. The flow in the fluid region is described by Stokes equations and in the poroelastic medium by the quasi-static Biot model. The focus of the model is on the quasi- Newtonian fluids that exhibit a shear-thinning property. We establish existence and uniqueness of the solution for two alternative formulations of the proposed model. Then we establish and show the existence and uniqueness of the solution of semidiscrete continuous-in-time formulation. We present complete stability and error analysis, as well as results of numerical simulations showing optimal rates of convergence for all variables. After that, the modeling of a transport equation in a non-linear Biot-Stokes flow will be analyzed. We use discontinuous Galerkin method to solve the transport equation. Several numerical tests are presented illustrating theoretical results and the capabilities of the method.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Nguyen, Truongtqn4@pitt.edutqn40000-0002-9249-6458
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairYotov, Ivanyotov@math.pitt.eduyotov
Committee MemberNeilan, Michaelneilan@pitt.eduneilan
Committee MemberLayton, Williamwjl@pitt.eduwjl
Committee MemberErvin,
Date: 26 September 2019
Date Type: Publication
Defense Date: 25 July 2019
Approval Date: 26 September 2019
Submission Date: 16 September 2019
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 122
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: non-linear, biot stokes, viscosity
Date Deposited: 26 Sep 2019 12:48
Last Modified: 26 Sep 2019 12:48


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