# Connections Between Regularized and Large-Eddy Simulation Methods for Turbulence (12w5063)

Arriving in Banff, Alberta Sunday, May 13 and departing Friday May 18, 2012

## Organizers

Eliot Fried (McGill University)

(University of Twente)

(University of Pittsburgh)

Robert Moser (University of Texas, Austin)

(Queen's University)

## Objectives

The primary objective of this workshop is to bring together mathematicians working on regularized models for turbulence and the most active and prominent mathematicians, fluid mechanicians, physicists, and computational scientists working on advanced, cutting-edge LES methods. As yet, interaction between these communities has been limited. This is mainly because their memberships use different terminology and notation. The workshop will foster communication between these two communities. This communication will allow for the identification of common ground, the cross-fertilization of ideas, and the specification of worthwhile problems. These developments should provide a foundation for many fruitful collaborations. These collaborations have the potential to lead to significant advances in our understanding of turbulence.

DNS is currently a highly useful research tool. Nevertheless, it is well-understood that it will be at least several decades before computer power will be sufficient to use DNS for practical applications. Fluid mechanicians agree strongly that, in the meantime, methods that, like DNS, resolve the most energetically significant modes of turbulent flow at computational costs lower than DNS provide the most promising alternatives to DNS. Regularized turbulence models share common features with DNS. Their mathematical structure provides a foundation for careful analysis. Such analysis should provide a foundation for the construction of improved LES models.

There are many significant questions that need to be addressed at this stage. Questions that will certainly be considered at the workshop include:

1. Where is the common ground between the two approaches? What are the distinguishing features of current regularized turbulence models? How do they agree with and differ from features of current LES models?

2. What general properties should regularized turbulence models possess?

3. To what extent should regularized models satisfy principles such as frame-indiffference and thermodynamic compatibility?

4. Is it possible to identify the subclass of regularized turbulence models that implicitly embody effective subfilter stresses?

5. For regularized turbulence models that do implicitly embody effective subfilter stresses, does the LES perspective provide insight regarding the physical nature of the underlying regularization?

6. How should boundary conditions for regularized equations such as the NS-$alpha$ equation, which involves fourth order spatial derivatives, be formulated?

7. For regularized models that give rise to higher-order evolution equations, what is the meaning of the additional boundary conditions at the subfilter level in the LES context?

8. Can advanced LES approaches such as the variational multiscale model be adapted to and implemented for regularized turbulence models.

9. To what extent should compatibility of models/regularizations and solution algorithms play in selection or development of LES?

We propose a 5-day workshop with approximately 32 senior participants (divided nearly equally between scientists who belong explicitly to departments of mathematics and scientists from other disciplines, supplemented with approximately 15 graduate students/postdocs.

Given the nature of the workshop, a few well-chosen speakers will present background material in the form of minicourses on LES and regularized turbulence models. These will occur during the morning and afternoon sessions of the first day. The second day and the morning session of the third day will be devoted to presentations of recent research results. With a view to establishing meaningful dialog, these sessions will purposely include presentations from members from both communities. A free afternoon on the third day is planned to allow participants to meet informally and to digest the information presented in the first half of the workshop. Regular presentations will reconvene that evening. The morning session of the fourth day will be devoted to discussions of opportunities for synergism, interdisciplinary work, and future interactions. Here, it is essential that an active discussion and interaction between the participants take place. The final day of the workshop will build on the discussions of the previous afternoon. Three of the senior, well-established, participants will be invited to give longer plenary style talks which set forth their vision of where their piece of the subject is, or should be, going. To close the workshop in a forward-looking manner, a brief summary session will also discuss future meetings and interactions.

The established participants listed below represent many of the world's leading or emerging experts in their areas of turbulence modeling. Naturally, many of these are younger faculty members and women. The majority of established participants listed have already been approached and have responded enthusiastically, expressing strong interest in participation. We are particularly delighted that this includes the physicists and engineers Carati, Hughes, and Moin, whose work is highly mathematical and has been central to modern advances in LES.