Integration of Geometric Sensitivity and Spatial Gradient Reconstruction for Aeroelastic Shape Optimization

Abstract

Continuum Sensitivity Analysis (CSA) provides an analytic method to obtain sensitivities of structural and fluid responses. Its primary advantages are that sensitivities are analytic and mesh sensitivity is avoided. CSA involves solving a set of Continuum Sensitivity Equations (CSEs) derived from the governing equations of the original analysis. Solution to CSE requires two terms: spatial gradients of the response and geometric sensitivity, also known as design velocity. Spatial gradients of the response may be obtained using Spatial Gradient Reconstruction (SGR) technique. In this paper we present complex step results for computing the geometric sensitivity from tools such as MstcGeom and VT-CST. Use of SGR in CSA makes amenable the non-intrusive implementation of CSA. In this paper, we describe the specific requirements of a fluid analysis code for non-intrusive implementation of CSA. The results of a survey of some flow solvers are presented that help choose a flow solver. Flow sensitivities of a lid-driven cavity are computed using CSA. This example illustrates that flow sensitivities of a nonlinear fluid system can be found accurately by CSA with just a change of the boundary conditions and source terms, while retaining the same discretization. Another example is presented to illustrate the use of the flow solver Stanford University Unstructured (SU2) for obtaining aeroelastic shape sensitivity. This example establishes the use of SU2 for aeroelastic analysis and to obtain its sensitivity by the CSA approach.