Adjoint Methods for Shape Optimization

In aerodynamic shape optimization, gradient-based methods often rely on the adjoint approach, which is capable of computing the objective function sensitivities with respect to the design variables. In the literature adjoint approaches are proved to outperform other relevant methods, such as the direct sensitivity analysis, finite differences or the complex variable approach. They appear in two different formulations, namely the continuous and the discrete one, which are both discussed in this chapter.

[1]  J. Peraire,et al.  Constrained, multipoint shape optimisation for complex 3D configurations , 1998, The Aeronautical Journal (1968).

[2]  L Bonhaus Daryl,et al.  Aerodynamic Design on Unstructured Grids for Turbulent , 1997 .

[3]  Juan J. Alonso,et al.  Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers , 1996 .

[4]  K. Giannakoglou,et al.  COMPRESSOR BLADE OPTIMIZATION USING A CONTINUOUS ADJOINT FORMULATION , 2006 .

[5]  Antony Jameson,et al.  Aerodynamic design via control theory , 1988, J. Sci. Comput..

[6]  D. Tortorelli,et al.  Design sensitivity analysis: Overview and review , 1994 .

[7]  M. Giles,et al.  Algorithm Developments for Discrete Adjoint Methods , 2003 .

[8]  Antony Jameson,et al.  Aero-Structural Wing Planform Optimization Using the Navier-Stokes Equations , 2004 .

[9]  Antony Jameson,et al.  Aerodynamic Shape Optimization of Complete Aircraft Configurations using Unstructured Grids , 2004 .

[10]  Antony Jameson,et al.  Control theory based airfoil design using the Euler equations , 1994 .

[11]  J. Peraire,et al.  Aerodynamic optimization of unstructured meshes with viscous effects , 1997 .

[12]  E. Nielsen,et al.  Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design , 2005 .

[13]  Niles A. Pierce,et al.  An Introduction to the Adjoint Approach to Design , 2000 .

[14]  Michael B. Giles,et al.  Analytic adjoint solutions for the quasi-one-dimensional Euler equations , 2001, Journal of Fluid Mechanics.

[15]  Oktay Baysal,et al.  Continuous Adjoint Sensitivities for Optimization with General Cost Functionals on Unstructured Meshes , 2001 .

[16]  A. Jameson,et al.  Design Optimization of High-Lift Configurations Using a Viscous Continuous Adjoint Method , 2002 .

[17]  Antony Jameson,et al.  NON-LINEAR FREQUENCY DOMAIN BASED OPTIMUM SHAPE DESIGN FOR UNSTEADY THREE-DIMENSIONAL FLOWS , 2006 .

[18]  O. Pironneau,et al.  SHAPE OPTIMIZATION IN FLUID MECHANICS , 2004 .

[19]  Kyriakos C. Giannakoglou,et al.  Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence , 2002 .

[20]  A. Jameson,et al.  Optimum Aerodynamic Design Using the Navier–Stokes Equations , 1997 .

[21]  Dimitri J. Mavriplis,et al.  A Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes , 2006 .

[22]  Ilan Kroo,et al.  Advanced Algorithms for Design and Optimization of Quiet Supersonic Platforms , 2002 .

[23]  J. Peraire,et al.  Practical Three-Dimensional Aerodynamic Design and Optimization Using Unstructured Meshes , 1997 .

[24]  Louis B. Rall,et al.  Automatic Differentiation: Techniques and Applications , 1981, Lecture Notes in Computer Science.

[25]  Juan J. Alonso,et al.  Automatic aerodynamic optimization on distributed memory architectures , 1996 .

[26]  Thomas Bäck,et al.  Evolutionary Algorithms in Theory and Practice , 1996 .

[27]  Bernard Grossman,et al.  Progressive optimization of inverse fluid dynamic design problems , 2000 .

[28]  M. D. Salas,et al.  Aerodynamic design and optimization in one shot , 1992 .

[29]  W. K. Anderson,et al.  Airfoil Design on Unstructured Grids for Turbulent Flows , 1999 .

[30]  W. K. Anderson,et al.  Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation , 1997 .

[31]  Juan J. Alonso,et al.  AIAA-2002-0261 An Adjoint Method for the Calculation of Remote Sensitivities in Supersonic Flow , 2002 .

[32]  M. Giles,et al.  Adjoint equations in CFD: duality, boundary conditions and solution behaviour , 1997 .

[33]  O. Pironneau.  Optimal Shape Design for Elliptic Systems , 1983 .

[34]  Volker Schulz,et al.  Simultaneous Pseudo-Timestepping for Aerodynamic Shape Optimization Problems with State Constraints , 2006, SIAM J. Sci. Comput..

[35]  S. Ta'asan,et al.  ANALYSIS OF THE HESSIAN FOR AERODYNAMIC OPTIMIZATION: INVISCID FLOW , 1996 .

[36]  Michael B. Giles,et al.  Discrete Adjoint Approximations with Shocks , 2003 .

[37]  Antony Jameson,et al.  Aero-Structural Wing Planform Optimization , 2004 .

[38]  A. Jameson,et al.  A COMPARISON OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACH TO AUTOMATIC AERODYNAMIC OPTIMIZATION , 2000 .

[39]  M. Sergio Campobasso,et al.  Adjoint Calculation of Sensitivities of Turbomachinery Objective Functions , 2003 .

[40]  Joel Brezillon,et al.  Aerodynamic shape optimization using simultaneous pseudo-timestepping , 2005 .

[41]  Jaime Peraire,et al.  Practical 3D aerodynamic design and optimization using unstructured meshes , 1996 .

[42]  Antony Jameson,et al.  Exploring the Limits of Shock-free Transonic Airfoil Design , 2005 .

[43]  A. Robin Forrest,et al.  Interactive interpolation and approximation by Bezier polynomials , 1972, Comput. J..

[44]  W. K. Anderson,et al.  Recent improvements in aerodynamic design optimization on unstructured meshes , 2001 .

[45]  Manuel D. Salas,et al.  Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization , 1997 .

[46]  Bernard Grossman,et al.  Fast convergence of inviscid fluid dynamic design problems , 2003 .

[47]  Kyriakos C. Giannakoglou,et al.  A continuous adjoint method with objective function derivatives based on boundary integrals, for inviscid and viscous flows , 2007 .

[48]  W. K. Anderson,et al.  Al A A-2001-0596 Recent Improvements in Aerodynamic Design Optimization On Unstructured Meshes , 2001 .

[49]  A. Jameson,et al.  Optimum Shape Design for Unsteady Three-Dimensional Viscous Flows Using a Nonlinear Frequency-Domain Method , 2006 .

[50]  Jaime Peraire,et al.  Aerodynamic design using unstructured meshes , 1996 .

[51]  Antony Jameson,et al.  Multi-point Wing Planform Optimization via Control Theory , 2005 .

[52]  E. Tadmor,et al.  Hyperbolic Problems: Theory, Numerics, Applications , 2003 .

[53]  Rainald Löhner,et al.  On the Boundary Computation of Flow Sensitivities , 2004 .

[54]  A. Jameson,et al.  Reduction of the Adjoint Gradient Formula in the Continuous Limit , 2003 .

[55]  Michael B. Giles,et al.  The harmonic adjoint approach to unsteady turbomachinery design , 2002 .

[56]  A. Jameson.  Optimum aerodynamic design using CFD and control theory , 1995 .

[57]  Juan J. Alonso,et al.  Two-dimensional High-Lift Aerodynamic Optimization Using the Continuous Adjoint Method , 2000 .

[58]  A. Jameson,et al.  STUDIES OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACHES TO VISCOUS AUTOMATIC AERODYNAMIC SHAPE OPTIMIZATION , 2001 .

[59]  D. I. Papadimitriou,et al.  Total pressure loss minimization in turbomachinery cascades using a new continuous adjoint formulation , 2007 .

[60]  M. D. Salas,et al.  Airfoil Design and Optimization by the One-Shot Method , 1995 .