Hybrid method for aerodynamic shape optimization in automotive industry Fr  ed erique Muyl a , Laurent Dumas b,1 , Vincent Herbert a, * a PSA Peugeot Citro€ en, Centre technique, 2 route de Gisy, BC VV013, 78943 V elizy Villacoublay, France b Laboratoire Jacques-Louis Lions, Universit e Pierre et Marie Curie, 4 place Jussieu, BC 87, 75005 Paris, France Received 29 July 2002; received in revised form 2 April 2003; accepted 4 June 2003 Abstract An aerodynamic shape optimization tool for complex industrial flows is developed, based on an hybrid process. The optimization method couples a stochastic genetic algorithm and a deterministic BFGS hill- climbing method. For each evaluation required by the optimizer, the Navier–Stokes equations with the k– turbulence model are solved with a commercial CFD code on an unstructured mesh surrounding the shape to optimize. After various validation test cases, the method is successfully applied to optimize the rear of a simplified car shape in order to bring acceleration in the computational time of the minimization of the drag coefficient. Ó 2003 Published by Elsevier Ltd. 1. Introduction Decreasing the fuel consumption of road vehicles, due to environmental and selling arguments reasons, concerns car manufacturers. Consequently, the improvement of the aerodynamics of car shapes, more precisely the reduction of their drag coefficient, becomes one of the main topics of the automotive research centers. As it has been shown that 40% of the drag coefficient depends on the external shape [1] and most of it on the rear of the geometry, a numerical optimization process is proposed here in order to seek innovative low-drag car shapes. The main objective of this study is to set up an optimization strategy for mono-disciplinary design problem using fluid mechanics * Corresponding author. Tel.: +33-1-57-59-39-69/54-21; fax: +33-1-57-59-21-77. E-mail addresses: frederique.muyl@mpsa.com (F. Muyl), dumas@ann.jussieu.fr (L. Dumas), vincent.herbert@ mpsa.com (V. Herbert). 1 Tel.: +33-1-44-27-85-19; fax: +33-1-44-27-72-00. 0045-7930/$ - see front matter Ó 2003 Published by Elsevier Ltd. doi:10.1016/j.compfluid.2003.06.007 Computers & Fluids 33 (2004) 849–858 www.elsevier.com/locate/compfluid