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Accurate prediction of fluids in motion: Attacking chaos, understanding turbulence and resolving complexity

Xu, Shuxian (2023) Accurate prediction of fluids in motion: Attacking chaos, understanding turbulence and resolving complexity. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Simulating fluid motion accurately and robustly is an enduring problem due to the com- plexity and chaotic nature of turbulent flows, the latter of which is often amplified by mea- surement errors in initial conditions. These challenges are deeply embedded in fluid flow simulations, making it a complex field that requires both efficient computing and accurate predictions. At the core of the unpredictability in fluid flow simulations is the exponential growth of errors until saturation, which stands as a formidable obstacle to the precision of predictions. Recognizing that extending the predictability horizon of simulations is possible through ensemble simulations, the thesis explores computational solutions to overcome the practical limitations tied to these methods.
Building on recent advances in the field, the research introduces improved ensemble algorithms centered around an optimized application of the penalty method. It presents novel solutions to the critical computational problems traditionally associated with the penalty method, namely increased matrix coupling, ill-conditioned systems, and sensitivity to parameter selection. By refining the penalty method, we manage to achieve ensemble simulations capable of handling larger sets with computational complexity comparable to a single realization.
The findings mark a significant stride towards accurate and efficient prediction of fluids in motion. By confronting turbulence and chaos in fluid behaviors head-on and adeptly managing the complexities inherent in fluid dynamics simulations, the research paves the way for enhanced predictive precision in the field. The novel methodologies and insights presented in this thesis will serve as invaluable resources for future investigations and applications in the diverse world of fluid dynamics.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Xu, Shuxianshx34@pitt.edushx340000-0003-2180-6348
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton,
Committee MemberTrenchea,
Committee MemberYotov,
Committee MemberJiang,
Date: 6 September 2023
Date Type: Publication
Defense Date: 27 June 2023
Approval Date: 6 September 2023
Submission Date: 11 July 2023
Access Restriction: 2 year -- Restrict access to University of Pittsburgh for a period of 2 years.
Number of Pages: 131
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: Navier-Stokes Equation, Penalty method, Sparse Grad-Div, Effective Con- dition Number, Adaptive, Ensemble Calculation
Date Deposited: 07 Sep 2023 01:33
Last Modified: 07 Sep 2023 01:33


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