Using A Fast and Explicit Mesh Movement Method To Efficiently Compute Mesh Sensitivity

A method based on the Delaunay graph mapping mesh movement is proposed to efficiently compute mesh sensitivity in the discrete adjoint optimisation framework. The method results in 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. The chain results in a straightforward computation of the surface mesh sensitivity without the need to invert a large sparse matrix generally associated with implicit mesh movements such as spring, torsional, truss and linear elastic analogy. The main finding is that the solution of the second linear mesh-adjoint system of equations is eliminated. The method was verified for the 2D RAE 5243 aerofoil and for the 3D ONERA M6 wing for two cases, (1) sensitivities against each surface mesh point as a design variable compared with finite differences and (2) sensitivities against incidence as a design variable compared with those derived analytically. A comparison with mesh movement using linear elasticity is also presented and reason for discrepancies proposed.