About this Event

29 Oxford Street, Cambridge, MA 02138

**Harvard John A. Paulson School of**

**Engineering and Applied Sciences**

WIDELY APPLIED MATHEMATICS SEMINAR

2 - 3pm

Pierce 301

**"Mathematical Modeling of Fluid Turbulence"**

**Professor Robert Moser, University of Texas at Austin**

**Abstract**: The modeling of the effects of turbulence in fluid flows is of great practical importance, as many technological devices involve turbulence. However, current turbulence models have numerous shortcomings, not the least of which is that they are unreliable. We are endeavoring to correct these shortcomings by addressing the fundamental mathematical and computational issues that cause them. We will discuss two different turbulence modeling approaches.

In large eddy simulation (LES), large scales of turbulence are defined through a filter operator, and the evolution of the filtered turbulence, including the effects the missing small scales, is modeled. Current LES models are generally formulated under restrictive assumptions that are not valid in realistic applications. We will discuss the effects of numerical discretization, anisotropy and inhomogeneity on LES modeling, along with theoretical tools we have used to investigate them.

In Reynolds-averaged Navier-Stokes (RANS) models, the evolution of the expected value of the velocity (mean) is modeled. Current RANS models are formulated to evolve a small number of statistical characteristics of the turbulence, in addition to the mean, which raises the question of what is a sufficient set of turbulence state variables to be able to predict their evolution. It has been hypothesized that a set of tensor fields (the structure tensors) are such a set. We will discuss our efforts to test that hypothesis by formulating models for critical terms in the evolution equations in terms of the structure tensors, using the theory of tensor invariants.

**Speaker Bio**: Robert D. Moser holds the W. A. “Tex” Moncrief Jr. Chair in Computational Engineering and Sciences and is professor in the Walker Department of Mechanical Engineering. He serves as the director of the Oden Institute's Center for Predictive Engineering and Computational Sciences (PECOS) and deputy director of the Oden Institute. Moser earned his Ph.D. in mechanical engineering from Stanford University. Before coming to The University of Texas at Austin, he was a research scientist at the NASA-Ames Research Center and then a professor of theoretical and applied mechanics at the University of Illinois.

Moser conducts research on the modeling and numerical simulation of turbulence and other complex fluid flow phenomena. He has been a leader in the use of direct numerical simulation for investigating and modeling turbulent flows, and the application of such direct simulations to the development of large eddy simulation models. He has also been active in the development of highly accurate high-resolution numerical approximations for use in simulation of turbulence and other complex flows. Finally, Moser has been working to develop new approaches for the validation of computational models and to assess their reliability.

Moser is a fellow of the American Physical Society, and was awarded the NASA Medal for Exceptional Scientific Achievement.