Many gradient based optimization methods can be found in the literature. If the input parameters of a cost function are subject to implicit constraints the adjoint method is often the preferred method to obtain the gradient. The adjoint method provides an efficient way for the computation of the gradient, where the computational time is independent of the number of control variables of the cost function.
In this work the noise of a three dimensional turbulent subsonic jet is minimized. The cost function is defined as an integral over the pressure fluctuations in the farfield and thus gives an estimate for noise emission. The simulations are based on the compressible Navier-Stokes equations, which act as implicit constraints for the minimization problem. The adjoint variables are computed using different approximations of the adjoint equations and the resulting gradient accuracy is investigated. Among other aspect the continuous and discrete adjoint methods are compared in terms of accuracy. Furthermore, the efficiency and effectivity of the optimization procedure is investigated in terms of gradient accuracy and numeric resolution.