Enhancement of Adjoint Design Methods for Aerodynamic Shape Optimization Problems

다국어 초록 (Multilingual Abstract)

Two independent approaches of enhancing adjoint design methods are presented in the paper. First, enhancing the Euler adjoint methods have been achieved by optimizing the adjoint parameters using a non-linear gradient-based optimization package, SNOPT. The Euler adjoint parameters include the coefficients of the residual smoothing scheme, the CFL numbers of the Euler and adjoint solutions, the implicit gradient smoothing coefficient, and the step size of the steepest descent method. The numerical results showed the feasibility of integration of the SNOPT package and the adjoint software in order to speed-up, improve and stabilize the performance of the design methods. Second, the paper presents a reduced adjoint gradient method using the both Euler and Navier-Stokes equations which reduces the computational cost of the gradients by transforming the volume integral part of the adjoint gradient formula into a surface integral. The savings are particularly significant for three-dimensional aerodynamic shape optimization problems. To validate the concept, the reduced gradient equations have been tested for various aerodynamic shape-optimization problems using the Euler equations.

목차 (Table of Contents)

• ABSTRACT
• INTRODUCTION
• PARAMETER OPTIMIZATION
• REDUCTION OF THE ADJOINT GRADIENT FORMULA
• CONCLUSION
• ACKOWLEDGEMENT
• REFERENCES