Reports on Large Eddy Simulation
and related topics including:
Finite Elements and Fluids
Subgrid-scale Modelling
High Reynolds Number Flow Problems

This is under construction.I am still learning!


Numerical Analysis of Large Eddy Simulation

   We are studying the mathematical development of large eddy simulation. Large eddy simulation (or LES) tries to predict the motion of the large structures in the turbulent flow of a fluid. LES has been highly developed by the engineering computational fluid dynamics community since its inception in 1970. The research program of our group at Pitt is to provide a mathematical and numerical analytic foundation for the field. In particular, it includes:

modeling-derivation of improved space filtered flow models,
                see the report with G.P.Galdi and the one with Iliescu,

asymptotics- improved boundary conditions for such models,

analysis- rigorous analytical study of the modeling error,

numerical analysis- derivation and validation of algorithms for space filtered models,

direct simulation- a new approach to LES of direct simulation of large eddies,

simulation- computational testing and benchmarking of the models and algorithms under study.

A New Variational Multiscale Method-

Approximate Deconvolution Models for Large Eddy Simulation-

     Understanding turbulent flow is central to many important problems including environmental and energy related applications (global change, mixing of fuel and oxidizer in engines and drag reduction), aerodynamics (maneuvering flight of jet aircraft) and biophysical applications (blood flow in the heart, especially the left ventricle). Turbulent flow is composed of coherent patches of swirling fluid called eddies. These range in size from large storm systems such as hurricanes to the little swirls of air shed from a butterflyĻs wings. Large Eddy Simulation (LES for short) seeks to predict the motion of the largest and most important eddies uncoupled from the small eddies. This uncoupling is important because the large eddies are resolvable on a computational mesh (a collection of chunks of the physical problem) which can be handled by a supercomputer.
    Our research involves modeling the large eddies (such as storm fronts, hurricanes and tornadoes in the atmosphere) in turbulent flow, predicting their motion in computational experiments and validating mathematically the large eddy models and algorithms developed. Current approaches to LES seem to be presently confronting some barriers to resolution, accuracy and predictability. It seems likely that many of these barriers can be traced to the mathematical foundation of the models used, the boundary conditions imposed and the algorithms employed for the simulations. The research undertaken is to develop these mathematical foundations as a guide for practical computation. This research promises to make it possible to extend the range of accuracy and reliability of predictions important to applications, such as those described above, where technological progress requires confronting turbulence! Click here to read more about our work-but check the reports!.