Physical Fidelity and Numerical Analysis of Turbulence Models

Monika Neda
Department of Mathematics, University of Pittsburgh

Abstract

This talk addresses the numerical study in which we bridge some of
the gap between mathematical theory and computational practices.
Accurate, efficient and reliable simulation of turbulent flows is
an essential difficulty in many current industrial applications.
Mathematical insights into physical fidelity of the turbulence
models of fluid will enable such simulations.

To that end, in the first part of my talk, I will present the
investigation of the physical fidelity of the approximate
deconvolution models by answering the questions: Do solutions of
the models exhibit an energy cascade and, if so, what are its
details? How do the models act to truncate the small eddies? and
What is the length scale of the smallest persistent eddy of the
models' solution? The joint helicity-energy cascade of the models
will also be presented.

In the second part of the talk, I will present a numerical analysis
of the Crank-Nicolson scheme for a recently proposed and attractive
family of high accuracy turbulence models. The analysis will be
followed by numerical experiments that confirm the convergence
theory and simulations of the 2-dimensional step problem.