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A continuous second‐order sensitivity equation method for time‐dependent incompressible laminar flows
Author(s) -
Ilinca F.,
Pelletier D.,
Borggaard J.
Publication year - 2007
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.1477
Subject(s) - strouhal number , laminar flow , reynolds number , mathematics , vortex shedding , sensitivity (control systems) , incompressible flow , convergence (economics) , compressibility , cylinder , flow (mathematics) , mathematical analysis , mechanics , geometry , turbulence , physics , economics , engineering , electronic engineering , economic growth
This paper presents a general formulation of the continuous sensitivity equation method (SEM) for computing first‐ and second‐order sensitivities of time‐dependent, incompressible laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The SEM formulation is verified on a problem with a closed‐form solution. Systematic grid convergence studies confirm the theoretical rates of convergence in both space and time. The methodology is then applied to uniform flow around a circular cylinder. The flow starts with a symmetrical solution and transitions to the traditional Von Karman street (alternate vortex shedding). Sensitivities are used to demonstrate fast evaluation of nearby flows. The accuracy of nearby flows is much improved when second‐order sensitivities are used. The sensitivity of the Strouhal number with respect to the Reynolds number agrees well with the computed and experimental St – Re relationship. Copyright © 2007 John Wiley & Sons, Ltd.