2014/01/16 by Patrick Blonigan, Blonigan, Patrick, Steven Gomez +3 · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #math.DS #nlin.CD #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1401.4163
Presented at AIAA Scitech 2014
arxiv created 2014/01/16 · openalex publication_date 2014/01/16 · arxiv updated 2014/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Computational methods for sensitivity analysis are invaluable tools for aerodynamics research and engineering design. However, traditional sensitivity analysis methods break down when applied to long-time averaged quantities in turbulent fluid flow fields, specifically those obtained using high-fidelity turbulence simulations. This is because of a number of dynamical properties of turbulent and chaotic fluid flows, most importantly high sensitivity of the initial value problem, popularly known as the "butterfly effect". The recently developed least squares shadowing (LSS) method avoids the issues encountered by traditional sensitivity analysis methods by approximating the "shadow trajectory" in phase space, avoiding the high sensitivity of the initial value problem. The following paper discusses how the least squares problem associated with LSS is solved. Two methods are presented and are demonstrated on a simulation of homogeneous isotropic turbulence and the Kuramoto-Sivashinsky (KS) equation, a 4th order chaotic partial differential equation. We find that while LSS computes fairly accurate gradients, faster, more efficient linear solvers are needed to apply both LSS methods presented in this paper to larger simulations.