Sensitivity analysis is a key element in a design optimization procedure. Although the related theory and numerical implementation are well known for steady problems, the application to unsteady partial differential equations, in particular in fluid mechanics, is still an active research area. In this report, a sensitivity equation method is described, in the context of compressible Navier-Stokes equations, and an efficient numerical implementation is proposed. The resulting approach is verified for two- and three-dimensional problems of increasing complexity.