Montestigliano Workshop 2011

Advanced optimization

techniques in fluid mechanics

3-9 April 2011, Montestigliano, Italy

Introduction

Numerical methods to solve the Navier-Stokes equations are well developed. However, to systematically analyze, optimize and control fluid flows, it is often necessary to find a way to approximate standard methods and algorithms, due to the complexity of the governing differential equations. Such approximations are are accomplished by incorporating methods and concepts from applied mathematics, such as control theory, numerical algebra, dynamical systems theory, etc. Previous Montestigliano workshops have introduced students to key concepts and recent advanced in model reduction and adjoint-based optimization to efficiently analyze and control fluid flows in complex geometries. The 4th Montestigliano workshop considers advanced techniques to solve optimization problems for differential equations, with a applications to fluid systems.

Derivate-free optimization

One type of advanced optimization method is the so called surrogate-based optimization framework. Three key issues, pertaining to fluid mechanics, will the be focused upon:

1. 1.How to extract as much information as possible about the n-dimensional optimization space from each (expensive) function evaluation, leveraging surrogate functions to “connect the dots” between existing functions evaluations.
   

2. 2.How to keep function evaluations as far apart as possible until convergence is approached to minimize the effect of noise in the function evaluations, leveraging n-dimensional sphere packings to coordinate the distribution of points in parameter space
   

3. 3.How to manage rigorously the issue of approximate function evaluations arising, e.g., from the DNS/LES of turbulent flows, in which the statistics of interest (drag, heat transfer, ...) in each simulation converge slowly (like the square root of the time dedicated thus far to that simulation).
   

References

16. P.Belitz and T. Bewley, “Efficient Derivate-free Optimization”, 46th IEEE Conf. on Decision Control, 2007
    

A. Booker, J. Dennis, P. Jr. Frank, D. Serafini, V. Torczon and M, Trosset. “A rigorous framework for optimization of expensive functions by surrogates”, Structural and Multidisciplinary Optimization, 17:113, 1999

Back to main page

Contact & organizers

Prof. Peter Schmid (LadHyx/École Polytechnique, France, email: peter@ladhyx.polytechnique.fr), Prof. Francois Gallaire (EPFL, Switzerland, email: francois.gallaire@epfl.ch), Dr. Fulvio Martinelli (LadHyx/École Polytechnique, France, fulvio.martinelli@ladhyx.polytechnique.fr) and Dr. Shervin Bagheri (KTH Sweden, shervin@mech.kth.se)