Journal
THEORETICAL AND APPLIED MECHANICS LETTERS
Volume 13, Issue 5, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.taml.2023.100472
Keywords
Acceleration method; Unsteady adjoint; Dynamic mode decomposition; Optimization efficiency
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In this letter, the authors propose a method to accelerate the solution of unsteady adjoint equations using dynamic mode decomposition (DMD). By approximating the pseudo-time marching as an infinite-dimensional linear dynamical system and analyzing the adjoint vectors using DMD, the efficiency of solving unsteady adjoint equations is significantly improved.
The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic optimization. In this letter, the solution of unsteady adjoint equations is accelerated by dynamic mode decomposition (DMD). The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system. Thereafter, DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching. First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step. Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example, the efficiency of solving unsteady adjoint equations is significantly improved. Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics, and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors, which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.
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