Shape Optimization Using an Adjoint Variable Method in ITBL Grid Environment

To decrease the fluid drag force on the surface of a specified object subjected to an unsteady flow, under a constant volume condition, the adjoint variable method is formulated by using FEM. Based on the Lagrange multiplier method (a conditional variational principle), this method consists of the state equation, the adjoint equation and the sensitivity equation. To solve the equations effectively using the steepest descent method, a parallel algorithm that finds the Armijo’s line-search step size is constructed. The shape optimization code for solving a large scale 3D problem using a parallel algorithm was implemented on ITBL [1,2] using the HPC-MW library [3]. Results show that, by using shape optimization, the fluid drag force on the object can be reduced by about 17.5%.