On consid ere l'application d'une m ethode de gradient au contrôle optimal d'un syst eme dont la simulation est coûteuse. Une strat egie s'inspirant des m ethodes multiniveau est appliqu ee pour travailler avec un nombre croissant de param etres. Cette strat egie est appliqu ee au probl eme acad emique de l'optimisation de la forme d'une tuy ere pour des ecoulements subsoniques et transsoniques r egis par les equations d'Euler.

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A numerical method for the simulation of 3D inviscid barotropic flows in rotating frames is presented. A barotropic state law incorporating a homogeneous-flow cavitation model is considered. The discretisation is based on a finite-volume formulation applicable to unstructured grids. A shock-capturing Roe-type upwind scheme is proposed for barotropic flows. The accuracy of the proposed method at low Mach numbers is ensured by ad-hoc preconditioning, preserving time consistency. An implicit time advancing only relying on the algebraic properties of the Roe flux function, and thus applicable to a variety of problems, is presented. The proposed numerical ingredients, already validated in a 1D context and applied to 3D non-rotating computations, are then applied to the 3D water flow around a typical turbopump inducer