Aerodynamic design optimization by the adjoint equation method on overset grids

Abstract

This paper deals with the use of the adjoint equation for aerodynamic shape optimization of complex configurations with overset grids methods. The use of overset grid eases the grid generation process, but the nontrivial task of ensuring communication between the overlapping grids needs careful attention. This need is effectively addressed by using a practically useful technique known as Implicit Hole Cutting (IHC) method first introduced by Lee and Baeder 1 and further demonstrated by the authors2 in a previous study. The method depends on the simplicity of the cell selection process based on the main criterion of cell size, and all grid points including hole interior points and hole fringe points are treated indiscriminately in the flow computation. The simplicity of the IHC method is exploited for the adjoint equation solver. Similar to the flow solver, the adjoint equations are solved on the conventional point-matched grids and overlapped grids within a multi-block framework. Parallel computing with MPI is also used to improve the overall efficiency of the design optimization process. The method is successfully applied to several two and three-dimensional shape optimization cases for both external and internal flows problems.