Efficient Method to Eliminate Mesh Sensitivity in Adjoint-Based Optimization

Abstract

A method based on the Delaunay graph mapping mesh movement is proposed to eliminate mesh sensitivity, which is required in the discrete adjoint optimization framework. The method makes use of a one-to-one explicit algebraic mapping between the volume and surface mesh nodes, for which the relative volume coefficients based on the Delaunay graph are computed only once. This procedure also results in a straightforward computation of the mesh sensitivity without the need to invert the large sparse matrix generally associated with implicit mesh movements such as the spring analogy, torsional spring, and linear elastic analogy. The advantage of the method comes from the fact that the solution of the second linear mesh adjoint system of equations is no longer required. The method has been verified for the two-dimensional RAE 5243 airfoil and for the three-dimensional ONERA M6 wing for two cases: 1) sensitivities of the objective function with respect to each surface mesh point as a design variable compared with those computed using finite differences, and 2) sensitivities against incidence as a design variable compared with those derived analytically. A comparison of the surface sensitivities with the mesh adjoint method using linear elasticity is also presented.