Carolina Manica

Finite Element Analysis of a Fundamental LES Model

We investigate stability and convergence of a semi-discrete finite element
method for the Zeroth Order LES Model. The filtering operation is
performed by the solution of a differential equation, so questions on how
this should be treated numerically and whether it affects the overall
solution are also addressed.

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Monika Neda 

Truncation of scales by time relaxation

We study a time relaxation regularization of flow problems proposed by 
Stolz and Adams. The aim of the relaxation term is to drive the unresolved 
fluctuations in a computational simulation to zero. Our aim is to 
understand how this term, by itself, acts to truncate solution scales and 
use this understanding to give insight into parameter selection.

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Leo Rebholz 

Conservation Laws in LES Models

Conservation of mass, momentum, energy, helicity and enstrophy in fluid 
flow is important because it is these quantities which organize a flow, 
and characterize change in the flow's structure over time.  Thus, if a 
simulation of a turbulent flow is to be qualitatively correct, these 
quantities should be conserved in the simulation.  However, such 
simulations are typically beased on turbulence models whose conservation 
properties are little explored and might be very different from those of 
the Navier-Stokes equations.

We explore conservation laws and approximate conservation laws satisfied 
by LES turbulence models.  For the Leray, Leray-deconvolution, Bardina, 
and N^{th} order approximate deconvolution models, we give exact or 
approximate laws for a model mass, momentum, energy, enstrophy and 
helicity.  Comparisons among the models are based on these laws.