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

Journal Article · Wed Nov 01 04:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.08.002· OSTI ID:22701627

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.

• OSTI ID: 22701627
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 348; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
COMPUTERIZED SIMULATION
DYNAMICAL SYSTEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SENSITIVITY ANALYSIS
THREE-DIMENSIONAL CALCULATIONS
TURBULENT FLOW