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Accuracy and Simplicity in One Equation Turbulence Models

Kean, Kiera (2022) Accuracy and Simplicity in One Equation Turbulence Models. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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The complex structure and dynamics of turbulence combined with computational limitations create a fundamental barrier. Turbulence is both rich in scale and chaotic in time, thus time accurate predictions of turbulent flows are out of reach for many important applications. If direct numerical simulations are not feasible, we turn to turbulence modeling. Unfortunately, many inexpensive popular models lack a strong theoretical backbone. We seek models that efficiently and accurately capture important flow characteristics. Eddy viscosity models, which model the effect of unresolved scales with enhanced dissipation, are the most commonly used today.

The scaling of the time averaged energy dissipation rate as U^3/L is fundamental, and has been proved mathematically and supported experimentally. Nonetheless, this law is violated in numerical tests of popular models. Numerical dissipation introduced by commonly used multistep methods is a potential cause or contributing factor. We explore the effects of numerical dissipation in multistep methods applied to the Navier-Stokes equations on this scaling. Additionally, any eddy viscosity models themselves may overdissipate, particularly in the presence of boundary layers. We look to create models that fit the true behavior of the underlying equations. By enforcing correct near wall behavior of the turbulent viscosity through a new turbulence length scale, we prevent overdissipation in the long time average while minimizing computational complexity. Motivated by enforcing model accuracy in the near wall area, the inclusion or exclusion of viscous diffusion in the k-equation is debated. By examining the derivation of the k-equation, we show that inclusion leads to incorrect near wall asymptotics.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Kean, Kierakkh16@pitt.edukkh16
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton,
Committee MemberNeilan,
Committee MemberYotov,
Committee MemberIyer,
Date: 11 October 2022
Date Type: Publication
Defense Date: 22 July 2022
Approval Date: 11 October 2022
Submission Date: 27 July 2022
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 120
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: Navier Stokes, turbulence models, computational fluid dynamics
Date Deposited: 11 Oct 2022 20:41
Last Modified: 11 Oct 2022 20:41

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  • Accuracy and Simplicity in One Equation Turbulence Models. (deposited 11 Oct 2022 20:41) [Currently Displayed]


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