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XIONG, XIN (2014) PARTITIONED METHODS FOR COUPLED FLUID FLOW AND TURBULENCE FLOW PROBLEMS. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Numerical simulation of different physical processes in different regions is one of the wide variety of real world applications. Many important applications such as coupled surface water groundwater flows require the accurate solution of multi-domain, multi-physics coupling of unobstructed flows with filtration or porous media flows. There are large advantages in efficiency, storage, accuracy and programmer effort in using partitioned methods build from components optimized for the individual sub-processes. On the other hand, the multi-domain or multi-physical process describes different natures of the physical processes of each subproblem. They may require different meshes, time steps and methods. There is a natural desire to uncouple and solve such systems by solving each sub physics problem, to reduce the technical complexity and allow the use of optimized, legacy sub-problems' codes in fluid flow. Stabilization using filters is intended to model and extract the energy lost to resolved scales due to nonlinearity breaking down resolved scales to unresolved scales. This process is highly nonlinear. Including a particular form of the nonlinear filter allows for easy incorporation of more knowledge into the filter process and its computational complexity is comparable to many of the current models which use linear filters to select the eddies for damping.

The objective of the first part of this work is the development, analysis and validation of new partitioned algorithms for some coupled flow models, addressing some of the above problems. Particularly, this thesis studies: i) long time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy sub problems, ii) analysis of a multi-rate splitting method for uncoupling evolutionary groundwater-surface water flows, and iii) a connection between filter stabilization and eddy viscosity models. For each problem, we give comprehensive analysis of stability and derive optimal error estimates of our proposed methods. Numerical experiments are performed to verify the theoretical results.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairWilliam , Laytonwjl@pitt.eduWJL
Committee MemberCatalin, Trencheatrenchea@pitt.eduTRENCHEA
Committee MemberIvan, Yotovyotov@math.pitt.eduYOTOV
Committee MemberMichael , Neilanneilan@pitt.eduNEILAN
Committee MemberPaolo, Zuninopaz13@pitt.eduPAZ13
Date: 30 May 2014
Date Type: Publication
Defense Date: 11 December 2013
Approval Date: 30 May 2014
Submission Date: 10 February 2014
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 130
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Applied Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Numerical Analysis, Scientific Computing, Finite Difference Methods, Finite Element Methods, Large Eddy Simulation, Porous Media Flows
Date Deposited: 30 May 2014 15:55
Last Modified: 15 Nov 2016 14:17


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