Sensitivity Analysis for Navier-Stokes Equations on Unstructured Meshes Using Complex Variables

TLDR: Although a step size parameter is required, the numerical derivatives are not subject to subtractive cancellation errors and, therefore, exhibit true second-order accuracy as the step size is reduced, in contrast to the use of finite differences.

Abstract: The use of complex variables for determining sensitivity derivatives for turbulent flows is examined. Although a step size parameter is required, the numerical derivatives are not subject to subtractive cancellation errors and, therefore, exhibit true second-order accuracy as the step size is reduced. As a result, this technique guarantees two additional digits of accuracy each time the step size is reduced one order of magnitude. This behavior is in contrast to the use of finite differences, which suffer from inaccuracies due to subtractive cancellation errors. In addition, the complex-variable procedure is easily implemented into existing codes