*As a professor of Mathematics at the University of Pittsburgh, Dr. Layton has advised 21 PhD students who are now all active researchers, many of which are working at research universities and are directing their own PhD students. Several of his students have won international prizes for their research accomplishments while studying with him. He has worked in various scientific areas and has authored more than 100 refereed publications. Layton’s research involves modeling the large eddies in turbulent flow, predicting their motion in computational experiments and validating mathematically the large eddy models and algorithms developed. The goal of Dr. Layton’s research is to develop these mathematical foundations as a guide for practical computation.
*

## Numerical Analysis of Turbulent Flows

### Friday, December 11, 2:30 – 3:30pm

### 1175 Benedum

Fluid flow is infinitely fascinating and complex. Turbulence also presents the oldest and most intractable multi-scale problem; turbulent flows contain a wide and almost continuous range of scales with no scale separation upon which reduced complexity models and simulations can be built.

“Numerical analysis” is concerned with models, methods, their validation and verification for the solution of problems (such as turbulent flows). This approach is especially difficult for turbulent flow problems and especially important for them because of (i) the enormous number of simulations performed every day with amazing color graphics and little correlation with real flows, and (ii) the wide array of critically important applications for which answers must be found.

This will be a general talk and have two parts. The first will be an overview about how to find reduced order models of high and provable accuracy for multi-scale applications (such as turbulent flows). The second part will give an overview of turbulent flows in two applications which present special difficulties for numerical simulations: coupled ocean-atmosphere climate simulations and simulations of turbulent flows inside pebble bed nuclear reactors. (The last two applications are surveys of the work of PhD students Jeff Connors and Ross Ingram.)