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On Approaches to Improving Reduced Descriptions of Fluid Flows

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Balu Nadiga (Los Alamos)

We start with a brief look at how fluid flow can be described using a
hierarchy of models of different complexities. Next, we consider
modeling of turbulent flows at two levels of the hierarchy and
pose a practical question of how a model of lower complexity can be
improved given simulations of the same flow that better resolves
some of the relevant processes. The specific context of
buoyancy-driven, variable-density turbulence is chosen for
illustration. In this context a Reynolds-stress turbulence closure
model is considered and analyzed given a few "fully-resolved" Direct
Numerical Simulations (DNS) of the flow. The task of improving the
closure model is currently the domain of turbulence modeling
experts. Are there alternatives? Computational?

There are a number of coefficients in the closure model associated
with various turbulent processes. Traditional approaches to
calibrating such coefficients are presented and their shortcomings
discussed. We then go on to demonstrate the potential of
hierarchical Bayesian analysis to uncover previously unanticipated
physical dependencies in the closure model---something that point
estimates fail to do, and how such insights can then be used to
improve the model. In effect parametric dependencies found from the
Bayesian analysis are used to improve structural aspects of the
model. This idea has wide applicability. Time permitting, related
issues and other applications will be considered.