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Direct sensitivity analysis for smooth unsteady compressible flows using complex differentiation
Author(s) -
Lu ShangYi,
Sagaut Pierre
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1386
Subject(s) - solver , compressibility , compressible flow , sensitivity (control systems) , computation , flow (mathematics) , mathematics , mixing (physics) , computational fluid dynamics , automatic differentiation , navier–stokes equations , mechanics , incompressible flow , computer science , physics , mathematical optimization , algorithm , engineering , electronic engineering , quantum mechanics
A method for the direct computation of the instantaneous sensitivities of unsteady compressible flows is proposed. It is based on the complex differentiation of the full compressible Navier–Stokes equations and does not require the storage of the unsteady flow solution to be differentiated. The method does not rely on any assumption on the basic Navier–Stokes solver, and can therefore be implemented in a straightforward way. The method is assessed on several cases, including a two‐dimensional subsonic mixing layer. It is observed that the sensitivity patterns can be interpreted thanks to Kovasznay's decomposition for perturbations in a compressible flow. Copyright © 2006 John Wiley & Sons, Ltd.