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

COUPLED SURFACE AND GROUNDWATER FLOWS: QUASISTATIC LIMIT AND A SECOND-ORDER, UNCONDITIONALLY STABLE, PARTITIONED METHOD

Moraiti, Marina (2015) COUPLED SURFACE AND GROUNDWATER FLOWS: QUASISTATIC LIMIT AND A SECOND-ORDER, UNCONDITIONALLY STABLE, PARTITIONED METHOD. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

[img]
Preview
PDF
Primary Text

Download (2MB)

Abstract

In this thesis we study the fully evolutionary Stokes-Darcy and Navier-Stokes/Darcy models for the coupling of surface and groundwater flows versus the quasistatic models, in which the groundwater flow is assumed to instantaneously adjust to equilibrium. Further, we develop and analyze an efficient numerical method for the Stokes-Darcy problem that decouples the sub-physics flows, and is 2nd-order convergent, uniformly in the model parameters.

We first investigate the linear, fully evolutionary Stokes-Darcy problem and its qua- sistatic approximation, and prove that the solution of the former converges to the solution of the latter as the specific storage parameter converges to zero. The proof reveals that the quasistatic problem predicts the solution accurately only under certain parameter regimes.

Next, we develop and analyze a partitioned numerical method for the evolutionary Stokes- Darcy problem. We prove that the new method is asymptotically stable, and second-order, uniformly convergent with respect to the model parameters. As a result, it can be used to solve the quasistatic Stokes-Darcy problem. Several numerical tests are performed to support the theoretical efficiency, stability, and convergence properties of the proposed method.

Finally, we consider the nonlinear Navier-Stokes/Darcy problem and its quasistatic ap- proximation under a modified balance of forces interface condition. We show that the solution of the fully evolutionary problem converges to the quasistatic solution as the specific stor- age converges to zero. To prove convergence in three spatial dimensions, we assume more regularity on the solution, or small data.


Share

Citation/Export:
Social Networking:
Share |

Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Moraiti, Marinamam328@pitt.eduMAM328
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, Williamwjl@pitt.eduWJL
Committee MemberTrenchea, Catalintrenchea@pitt.eduTRENCHEA
Committee MemberPan, Yibiaoyibiao@pitt.eduYIBIAO
Committee MemberAbad, Jorgejabad@pitt.eduJABAD
Date: 27 September 2015
Date Type: Publication
Defense Date: 2 December 2014
Approval Date: 27 September 2015
Submission Date: 18 June 2015
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 210
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: Subsurface flow, surface flow, groundwater, coupled flow, Stokes, Darcy, Navier-Stokes, porous media, aquifer, specific storage, hydraulic conductivity, small parameters, fully evolutionary, quasistatic limit, numerical methods, partitioned schemes, decoupled schemes, energy stability, unconditional stability, error analysis, convergence rate, second-order method, numerical simulation
Date Deposited: 27 Sep 2015 22:51
Last Modified: 15 Nov 2016 14:28
URI: http://d-scholarship.pitt.edu/id/eprint/25088

Metrics

Monthly Views for the past 3 years

Plum Analytics


Actions (login required)

View Item View Item