Computation of Design Sensitivities in Steady-State Incompressible Laminar Flows Based on New Semi-Analytical Method

In this paper, a new semi-analytic method (SAM) is proposed as a robust and efficient approach based on complex variables to compute the sensitivity of steady-state incompressible laminar flows. This method combines the complex variable method (CVM) via the discrete sensitivity analysis in order to obtain the sensitivity of response accurately and efficiently. The governing Navier–Stokes equations are solved using the finite element method and then new SAM is employed. The proposed procedure retains the computational efficiency of SAM with higher accuracy. In addition, the scheme is not sensitive to the step size, a characteristic that eases its application in practical problems. It is proved that the discrete sensitivity analysis is equivalent to CVM and solves the same equation. Finally, the accuracy of the method is investigated through various numerical cases compared to other methods and reveals that this scheme is reliable and independent to the step size. The proposed approach is applicable to a wide range of engineering problems.