A continuous second‐order sensitivity equation method for time‐dependent incompressible laminar flows

Ilinca, F.; Pelletier, Dominique; Borggaard, Jeff

doi:10.1002/fld.1477

Cited by 7 publications

(8 citation statements)

References 28 publications

(26 reference statements)

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“…In our previous work [26], the numerical approach was verified using the method of manufactured solutions [28]. In such a case, the direct differentiation of the manufactured solution provides closed-form expressions for the sensitivities.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The grid and time-step refinement study showed that the flow and sensitivity solutions are accurate and the algorithm recovers the theoretical grid convergence rate. The sensitivity solution can also be verified by estimating the flow gradients with respect to a using FDs [3,26]. For this, the design parameter a is changed by a small amount a and the solution is recomputed.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The error in the FDs gradient depends on the magnitude of high-order derivatives, which increase at a faster rate than the solution and its first-order derivative. Hence, the FD sensitivity is reliable only in the first few instants of the simulation, when higher-order terms are negligible [26].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Velocity and pressure are discretized using equal-order interpolations (P1-P1 tetrahedral elements) and equations are solved by a streamline-upwind Petrov Galerkin (SUPG) finite element method [26].…”

Section: Flow Equationsmentioning

confidence: 99%

“…This body of work has shown that sensitivities provide an enriched basis of information on which to develop an understanding of complex flow problems. The method was further extended to transient laminar flow by Hristova et al [25], and Ilinca et al [26] and to shape parameters of unsteady flows by Ilinca et al [3] and Ilinca and Pelletier [27]. This paper presents a formulation of the SEM valid for value and shape parameters and applicated to steady and unsteady laminar flows.…”

Section: Introductionmentioning

confidence: 98%

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First‐ and second‐order sensitivity equation methods for value and shape parameters

Ilinca

Pelletier

Hay

2008

Numerical Methods in Fluids

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SUMMARYThis paper presents formulations of the sensitivity equation method (SEM) and applications to transient flow problems. Solutions are shown for both value and shape parameters using a three-dimensional solution algorithm. Sensitivities are used for fast evaluation of the flow at nearby values of the parameters: the solution is approximated by a Taylor series in parameter space involving the flow sensitivities. The accuracy of nearby flows is much improved when second-order sensitivities are used. We show how the sensitivity of the Strouhal number can be obtained from the flow sensitivities. Results are in agreement with the experimental correlation. The methodology is also applied to the flow past a cylinder in ground proximity. The proposed method is verified on a steady-state problem by comparing the computed sensitivity with the actual change in the solution when a small perturbation is imposed on the shape parameter. We then investigate the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. The approach properly reproduces the damping or amplification of the vortex shedding with a reduction or increase of the gap size.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Flow Equationsmentioning

confidence: 99%