Adjoint sensitivity analysis of steady laminar flows with respect to nongeometrical parameters

Abstract

This work explores an alternative approach to computing sensitivity (derivatives) of functionals with respect to a broader range of control parameters in fluid flow problems. It builds upon the complementary character of the boundary problems that underlie the flow and the corresponding adjoint equations. Such complementarity is used to ensure well-posedness of the latter, which then yields a solution that conveys information on a broad range of sensitivities. This formulation of the boundary problem can extend the range of applications of the adjoint method to a host of new possibilities. The methodology is applied to internal and external laminar steady flows and the results are compared to those obtained with a finite-difference approach. Good agreement is observed in all cases, which demonstrates the correctness and applicability of the method.