Aerodynamic turbomachinery optimization using CFD requires to deal with large numbers of design parameters, today about 100 to 1000. On the other hand, the computational effort still has to be affordable, e.g. a few days on a high performance cluster. Because of the high computational cost, with conventional methods it is hardly possible to vary that many parameters.
The adjoint method allows the computation of sensitivities (derivatives) of flow variables or quantities derived from them with respect to geometrical parameters. This is more efficient than the direct computation of derivatives from flow solutions, e.g. by finite differences, if the number of parameters is large compared to the number of objective functionals. Since only one adjoint solution has to be computed for each functional, the cost for a sensitivity calculation for z objective functionals is independent of the number d of design parameters and the resulting speedup is z/d.
For the implementation in TRACE the discrete adjoint RANS equations are used.