Feasibility analysis of ensemble sensitivity computation in turbulent flows
Abstract
In chaotic systems, such as turbulent flows, the solutions to tangent and adjoint equations exhibit an unbounded growth in their norms. This behavior renders the instantaneous tangent and adjoint solutions unusable for sensitivity analysis. The Lea-Allen-Haine ensemble sensitivity (ES) estimates provide a way of computing meaningful sensitivities in chaotic systems by utilizing tangent/adjoint solutions over short trajectories. In this paper, we analyze the feasibility of ES computations under optimistic mathematical assumptions on the flow dynamics. Furthermore, we estimate upper bounds on the rate of convergence of the ES method in numerical simulations of turbulent flow. Even at the optimistic upper bound, the ES method is computationally intractable in each of the numerical examples considered.
Keywords
Cite
@article{arxiv.1811.08567,
title = {Feasibility analysis of ensemble sensitivity computation in turbulent flows},
author = {Nisha Chandramoorthy and Pablo Fernandez and Chaitanya Talnikar and Qiqi Wang},
journal= {arXiv preprint arXiv:1811.08567},
year = {2020}
}
Comments
30 pages, AIAA journal preprint