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The combustion efficiency of direct injection engines is largely dependent upon the mixing of fuel in air, thereby creating a combustible mixture. Such a process is highly dependent upon the motion of the charge in the cylinder. The shape of the intake runners and valves determines the charge motion generated within the engine. Swirl and tumble, generated along the vertical and horizontal axis respectively, govern the charge motion and hence distribution of combustible mixture. Unlike traditional parametric optimization where the parameter space has to be predetermined, adjoint optimization utilizes the gradient of objective functions obtained from a computational fluid dynamics solution to modify the shape of the original CAD geometry. During the optimization process, specific parts of the geometry can be morphed in any direction freely. The final design is a fluid volume generated as a result of such adjoint computations.

Understanding the flow characteristics and, especially, how the aerodynamic forces are influenced by the changes in the vehicle body shape, are very important in order to improve vehicle aerodynamics. One specific goal of aerodynamic shape optimization is to predict the local shape sensitivities for aerodynamic forces. The availability of a reliable and efficient sensitivity analysis method will help to reduce the number of design iterations and the aerodynamic development costs. Among various shape optimization methods, the Adjoint Method has received much attention as an efficient sensitivity analysis method for aerodynamic shape optimization because it allows the computation of sensitivity information for a large number of shape parameters simultaneously.