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.

本文提出了一种新的半解析方法（SAM），它是一种基于复杂变量的稳健而有效的方法，用于计算稳态不可压缩层流的灵敏度。该方法通过离散敏感度分析将复变量方法（CVM）组合在一起，以便准确，有效地获得响应的敏感度。用有限元方法求解控制Navier–Stokes方程，然后采用新的SAM。所提出的过程以更高的精度保留了SAM的计算效率。另外，该方案对步长不敏感，这是易于在实际问题中应用的特征。证明了离散灵敏度分析等效于CVM并求解相同的方程。最后，与其他方法相比，通过各种数值案例研究了该方法的准确性，结果表明该方案可靠且独立于步长。所提出的方法适用于广泛的工程问题。