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Pakzad, Ali (2018) ENERGY DISSIPATION IN TURBULENCE. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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The accurate simulation of turbulent flows is a central computational challenge in many important applications, including global climate change estimation, environmental science, ocean and atmosphere dynamics, energy efficiency improvement and optimization of industrial
processes. As an example, turbulence predictions are key to limiting the damage of hurricanes (estimated to be hundreds of billions of dollars in 2017). These are fundamentally non-linear problems that probed in this thesis through numerical computations and supporting mathematical analysis. The accuracy of turbulence models depends on their turbulent
dissipation. The dissipation is studied and it is utilized to validate results with the Statistical Equilibrium Law as the benchmark:

- In Chapter 3, the energy dissipation in a turbulence model discretized on an underresolved mesh is delineated. This is the first connection between computational experience and mathematical analysis in this direction [63].

-It is rigorously proved in Chapter 4 that the over-dissipation (wrong accuracy) of a turbulence model can be corrected using van Driest damping [62]. This had been an open question (e.g. [5] p. 78) since 1963.

-The temperature in natural convection is uniformly bounded in time. Although the problem has been studied for a long time, no better bounds for the approximate temperature than an exponential growth in time were obtained e.g. [78, 79, 87]. In Chapter 5, it is proved that the temperature approximation is bounded sub-linearly in time by introducing a new interpolation [19].


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Pakzad, Alialp145@pitt.edualp145
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton,
Committee MemberNeilan,
Committee MemberTrenchea,
Committee MemberIyer,
Date: 27 September 2018
Date Type: Publication
Defense Date: 10 May 2018
Approval Date: 27 September 2018
Submission Date: 9 June 2018
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 99
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: Turbulence, Energy Dissipation, Navier-Stokes Equations, Smagorinsky Model, Large Eddy Simulation, Over-Dissipation, Damping Function, Energy Cascade, Statistical Equilibrium, Stability, Finite Element Method, Hopf Interpolation, Natural Convection
Date Deposited: 27 Sep 2018 20:14
Last Modified: 27 Sep 2018 20:14

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