Derivatives for Time-Spectral Computational Fluid Dynamics Using an Automatic Differentiation Adjoint

sensitivities for an oscillating ONERA M6 wing. The sensitivities are shown to be accurate to 8–12 digits, and the computational cost of the adjoint computations is shown to scale well up to problems of more than 41 million state variables.

[1]  O. Pironneau.  On optimum design in fluid mechanics , 1974 .

[2]  Bengt Fornberg,et al.  Numerical Differentiation of Analytic Functions , 1981, TOMS.

[3]  Louis B. Rall,et al.  Automatic differentiation , 1981 .

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

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

[6]  C. Bendtsen.  FADBAD, a flexible C++ package for automatic differentiation - using the forward and backward method , 1996 .

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

[8]  M. J. Rimlinger,et al.  Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers , 1997 .

[9]  J. Eric,et al.  Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations , 1998 .

[10]  Dafydd Gibbon,et al.  1 User’s guide , 1998 .

[11]  George Trapp,et al.  Using Complex Variables to Estimate Derivatives of Real Functions , 1998, SIAM Rev..

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

[13]  M. J. Rimlinger,et al.  Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers , 1997 .

[14]  B. I. Soemarwoto,et al.  Airfoil design and optimization methods: recent progress at NLR , 1999 .

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

[16]  Andreas Griewank,et al.  Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation , 2000, TOMS.

[17]  W. K. Anderson,et al.  Sensitivity Analysis for Navier-Stokes Equations on Unstructured Meshes Using Complex Variables , 2001 .

[18]  Jeffrey P. Thomas,et al.  Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique , 2002 .

[19]  T. Pulliam,et al.  Multipoint and Multi-Objective Aerodynamic Shape Optimization , 2002 .

[20]  Juan J. Alonso,et al.  SONIC BOOM REDUCTION USING AN ADJOINT METHOD FOR WING-BODY CONFIGURATIONS IN SUPERSONIC FLOW , 2002 .

[21]  Joaquim R. R. A. Martins,et al.  High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet , 2002 .

[22]  D. Zingg,et al.  Newton-Krylov Algorithm for Aerodynamic Design Using the Navier-Stokes Equations , 2002 .

[23]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[24]  Laurent Hascoët,et al.  TAPENADE 2.1 user's guide , 2004 .

[25]  Lee,et al.  [American Institute of Aeronautics and Astronautics 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Austin, Texas ()] 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Aeroelastic Studies on a Folding Wing Configuration , 2005 .

[26]  Jeffrey P. Thomas,et al.  Discrete Adjoint Approach for Modeling Unsteady Aerodynamic Design Sensitivities , 2005 .

[27]  J. Alonso,et al.  A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design , 2005 .

[28]  Antony Jameson,et al.  Time Spectral Method for Periodic Unsteady Computations over Two- and Three- Dimensional Bodies , 2005 .

[29]  A. Jameson,et al.  Turbomachinery Applications with the Time Spectral Method , 2005 .

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

[31]  Juan J. Alonso,et al.  High-Speed MHD Flow Control Using Adjoint-Based Sensitivities , 2006 .

[32]  Juan J. Alonso,et al.  Demonstration of Nonlinear Frequency Domain Methods , 2006 .

[33]  Antony Jameson,et al.  The computational efficiency of non-linear frequency domain methods , 2006, J. Comput. Phys..

[34]  J. Alonso,et al.  ADjoint: An Approach for the Rapid Development of Discrete Adjoint Solvers , 2006 .

[35]  Georgi Kalitzin,et al.  Unsteady turbomachinery computations using massively parallel platforms , 2006 .

[36]  Antony Jameson,et al.  Optimum Shape Design for Unsteady Flows with Time-Accurate Continuous and Discrete Adjoint Methods , 2007 .

[37]  J. Alonso,et al.  A methodology for the development of discrete adjoint solvers using automatic differentiation tools , 2007 .

[38]  Kivanc Ekici,et al.  Nonlinear Analysis of Unsteady Flows in Multistage Turbomachines Using Harmonic Balance , 2007 .

[39]  A. Gopinath,et al.  Efficient fourier-based algorithms for time-periodic unsteady problems , 2007 .

[40]  David W. Zingg,et al.  Numerical aerodynamic optimization incorporating laminar-turbulent transition prediction , 2007 .

[41]  Jason E. Hicken,et al.  Parallel Newton-Krylov Solver for the Euler Equations Discretized Using Simultaneous-Approximation Terms , 2008 .

[42]  Dimitri J. Mavriplis,et al.  Unsteady Discrete Adjoint Formulation for Two-Dimensional Flow Problems with Deforming Meshes , 2008 .

[43]  D. Mavriplis.  Solution of the Unsteady Discrete Adjoint for Three-Dimensional Problems on Dynamically Deforming Unstructured Meshes , 2008 .

[44]  Gianluca Iaccarino,et al.  Helicopter Rotor Design Using a Time-Spectral and Adjoint-Based Method , 2008 .

[45]  M. Rumpfkeil,et al.  The optimal control of unsteady flows with a discrete adjoint method , 2010 .

[46]  Beckett Yx Zhou,et al.  Airfoil Optimization Using Practical Aerodynamic Design Requirements , 2010 .

[47]  Dimitri J. Mavriplis,et al.  Adjoint Sensitivity Formulation for Discontinuous Galerkin Discretizations in Unsteady Inviscid Flow Problems , 2010 .

[48]  A. N. Other.  A demonstration of the L A T E X2ε class file for the International Journal for Numerical Methods in Fluids , 2010 .

[49]  Jason E. Hicken,et al.  Induced-Drag Minimization of Nonplanar Geometries Based on the Euler Equations , 2010 .

[50]  C. Mader,et al.  Computation of Aircraft Stability Derivatives Using an Automatic Differentiation Adjoint Approach , 2011 .

[51]  Jeffrey P. Thomas,et al.  Discrete Adjoint Method for Nonlinear Aeroelastic Sensitivities for Compressible and Viscous Flows , 2013 .

[52]  C. Mader,et al.  Stability-Constrained Aerodynamic Shape Optimization of Flying Wings , 2013 .

[53]  John T. Hwang,et al.  Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models , 2013 .

[54]  Slawomir Koziel,et al.  Multi-objective Airfoil Design Using Variable-Fidelity CFD Simulations and Response Surface Surrogates , 2014 .