Multilevel strategies for parametric shape optimization in aerodynamics

Badr Abou El Majd (1) , Jean-Antoine Desideri (1) , Régis Duvigneau (2)

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

The essential numerical features of multilevel strategies developed for parametric shape optimization are reviewed. These methods employ nested parameterization supports of either shape, or shape deformation, and the classical process of degree elevation resulting in exact geometrical data transfer from coarse to fine representations. The algorithms mimick classical multigrid strategies and are found very effective in terms of convergence acceleration. In particular, for a drag reduction problem involving a three-dimensional Eulerian transonic flow simulated by an unstructured-grid finite-volume method, the complete algorithm is found to be noticeably superior to the natural algorithm simply based on progressive degree elevation.

Mots clés: Optimum shape design; compressible aerodynamics; finite–volume methods; shape parameterization; multilevel algorithms

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

Badr Abou El Majd, Jean-Antoine Desideri, Régis Duvigneau. Multilevel strategies for parametric shape optimization in aerodynamics. Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, 2008, 17 (1-2). ⟨hal-01730520⟩