A sensitivity equation method for fast evaluation of nearby flows and uncertainty analysis for shape parameters

Régis Duvigneau (1) , Dominique Pelletier (2)

1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
2 EPM - École Polytechnique de Montréal

This paper presents the application of the Continuous Sensitivity Equation Method (CSEM) to fast evaluation of nearby flows and to uncertainty analysis for shape parameters. The flow and sensitivity fields are solved using an adaptive finite-element method. A new approach is presented to extract accurate flow derivatives at the boundary, which are needed in the shape sensitivity boundary conditions. Boundary derivatives are evaluated via high order Taylor series expansions used in a constrained least-squares procedure. The proposed method is first applied to fast evaluation of nearby flows: the baseline flow and sensitivity fields around a NACA 0012 airfoil are used to predict the flow around airfoils with nearby shapes obtained by modifications of the thickness (NACA 0015), the angle of attack and the camber (NACA 4512). The method is then applied to evaluate the influence of geometrical uncertainties on the flow around a NACA 0012 airfoil.

Mots clés: Continuous Sensitivity Equation Method; fast evaluations of nearby flows; uncertainty analysis; sensitivity analysis

Domaines: Mécanique des fluides [physics.class-ph]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [cs.NA]

Régis Duvigneau, Dominique Pelletier. A sensitivity equation method for fast evaluation of nearby flows and uncertainty analysis for shape parameters. International Journal of Computational Fluid Dynamics, 2006, 20 (7). ⟨hal-01730821⟩