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Title: Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing

Abstract

This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow. - Highlights: • A discrete adjoint non-intrusive least squares shadowing (NILSS) is presented. • The NILSS approach is closely related to multiple shooting shadowing (MSS). • Adjoint NILSS prevents exponential growth in time of the adjoint field. • Adjoint NILSS is demonstrated on a simulation of wall-bounded turbulent flow.

Authors:
Publication Date:
OSTI Identifier:
22701627
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 348; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; COMPUTERIZED SIMULATION; ONE-DIMENSIONAL CALCULATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SENSITIVITY ANALYSIS; THREE-DIMENSIONAL CALCULATIONS; TURBULENT FLOW; DYNAMICAL SYSTEMS

Citation Formats

Blonigan, Patrick J., E-mail: patrick.j.blonigan@nasa.gov. Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.08.002.
Blonigan, Patrick J., E-mail: patrick.j.blonigan@nasa.gov. Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing. United States. doi:10.1016/J.JCP.2017.08.002.
Blonigan, Patrick J., E-mail: patrick.j.blonigan@nasa.gov. Wed . "Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing". United States. doi:10.1016/J.JCP.2017.08.002.
@article{osti_22701627,
title = {Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing},
author = {Blonigan, Patrick J., E-mail: patrick.j.blonigan@nasa.gov},
abstractNote = {This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow. - Highlights: • A discrete adjoint non-intrusive least squares shadowing (NILSS) is presented. • The NILSS approach is closely related to multiple shooting shadowing (MSS). • Adjoint NILSS prevents exponential growth in time of the adjoint field. • Adjoint NILSS is demonstrated on a simulation of wall-bounded turbulent flow.},
doi = {10.1016/J.JCP.2017.08.002},
journal = {Journal of Computational Physics},
number = ,
volume = 348,
place = {United States},
year = {Wed Nov 01 00:00:00 EDT 2017},
month = {Wed Nov 01 00:00:00 EDT 2017}
}