A continuous shape sensitivity equation method for unsteady laminar flows

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DOIResolve DOI: http://doi.org/10.1080/10618560701649952
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Journal titleInternational Journal of Computational Fluid Dynamics
Pages255266; # of pages: 12
SubjectShape sensitivity; Flow control; Finite elements; Unsteady flows
AbstractThis paper presents the application of a general shape sensitivity equation method (SEM) to unsteady laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The flow and sensitivity equations are solved on 3D meshes using a Streamline-Upwind Petrov Galerkin (SUPG) finite element method. In the case of shape parameters, boundary conditions for sensitivities depend on the flow gradient at the boundary. Therefore, an accurate recovery of solution gradients is crucial to the success of shape sensitivity computations. In this work, solution gradients at boundary points are extracted using the Finite Node Displacement (FiND) method on which the finite element discretization is enriched locally via the insertion of nodes close to the boundary points. The normal derivative of the solution is then determined using finite differences. This approach to evaluate shape sensitivity boundary conditions is embedded in the continuous SEM. The methodology is applied to the flow past a cylinder in ground proximity. First, the proposed method is verified on a steady state problem. The computed sensitivity is compared to the actual change in the solution when a small perturbation is imposed to the shape parameter. Then, the study investigates the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. A reduction of the gap causes damping of the vortex shedding while an increase amplifies the unsteadiness.
Publication date
AffiliationNational Research Council Canada (NRC-CNRC); NRC Industrial Materials Institute
Peer reviewedYes
NRC number49394
NPARC number15795091
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Record identifier6ce39761-b780-4863-a370-a37d19d19a7f
Record created2010-07-09
Record modified2016-05-09
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