Optimization with LES -- algorithms for dealing with sampling error of turbulence statistics

Abstract

Optimization with Large Eddy Simulations (LES) can be challenging due to noisy objective function. This noise is because of the sampling error of turbulent statistics. It decays slowly as computation cost increases, therefore is significant in most simulations. It is often unpredictable due to chaotic dynamics of turbulence, in that it can be totally different for almost identical simulations. In this paper we evaluate several optimization algorithms that are designed to handle noisy objective functions by testing it on the Lorenz equations, a low dimensional chaotic dynamical system. Bayesian optimization, one of the better performing algorithms, is then adapted to minimize drag in a turbulent channel flow. Our optimization algorithm simultaneously runs several simulations, each parallelized to thousands of cores, in order to utilize additional concurrency offered by today’s supercomputers.