Effect of grid displacement models on sensitivity derivatives computed by the continuous adjoint method in aerodynamic and conjugate heat transfer shape optimization

Abstract

ABSTRACT For aerodynamic and conjugate heat transfer problems, the work reported in this article investigated the effect of the grid displacement model on the derivatives of an objective function with respect to the design variables. A comparison was made in the first step of the study between reference sensitivity derivatives computed by finite differences and different grid displacement models (volumetric B-splines, Laplace partial differential equations, Delaunay graphs and inverse distance weighting). Then, a continuous adjoint method including the adjoint to the Laplace grid displacement model was used to recompute sensitivity derivatives. To shed more light and to support the authors' findings, an alternative continuous adjoint method for computing the objective function gradient in terms of the field integrals of grid sensitivities was also formulated and programmed. Finally, the effect of an inconsistent differentiation of the grid displacement model on the optimized solution was investigated. The choice of the grid displacement model did not affect the sensitivity derivatives in any of the cases examined.