Aerodynamic shape optimization using preconditioned conjugate gradient methods

In an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures, a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure. It is demonstrated that preconditioned conjugate gradient-like methodologies dramatically decrease the computational efforts required for such procedures. The design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric (NACA 0012) airfoil in inviscid transonic flow and at zero degrees angle of attack. The complete surface shape is represented using a Bezier-Bernstein polynomial

[1]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[2]  Oktay Baysal,et al.  Improving the efficiency of aerodynamic shape optimization , 1994 .

[3]  Garret N. Vanderplaats,et al.  Numerical Optimization Techniques for Engineering Design: With Applications , 1984 .

[4]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[5]  G. Vanderplaats,et al.  Structural optimization by methods of feasible directions. , 1973 .

[6]  D. Whitfield,et al.  Discretized Newton-relaxation solution of high resolution flux-difference split schemes , 1991 .

[7]  S. R. Chakravarthy,et al.  Relaxation methods for unfactored implicit upwind schemes , 1984 .

[8]  V. Korivi,et al.  Sensitivity analysis, approximate analysis, and design optimization for internal and external viscous flows , 1991 .

[9]  O. Baysal,et al.  Aerodynamic Sensitivity Analysis Methods for the Compressible Euler Equations , 1991 .

[10]  Paul D. Orkwis,et al.  Comparison of Newton's and quasi-Newton's method solvers for the Navier-Stokes equations , 1993 .

[11]  H. Elbanna,et al.  Determination of aerodynamic sensitivity coefficients based on the transonic small perturbation formulation , 1990 .

[12]  Andreas Griewank,et al.  Automatic Differentiation of Advanced CFD Codes for Multidisciplinary Design , 1992 .

[13]  Oktay Baysal,et al.  Airfoil Shape Optimization Using Sensitivity Analysis on Viscous Flow Equations , 1993 .

[14]  H. Elbanna,et al.  Determination of aerodynamic sensitivity coefficients in the transonic and supersonic regimes , 1989 .

[15]  Oktay Baysal,et al.  Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics , 1991 .

[16]  V. Venkatakrishnan.  Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations , 1990 .

[17]  O. Axelsson,et al.  Preconditioned Conjugate Gradient Methods , 1990 .

[18]  B. V. Leer,et al.  Experiments with implicit upwind methods for the Euler equations , 1985 .

[19]  Yousef Saad,et al.  Solving Sparse Triangular Linear Systems on Parallel Computers , 1989, Int. J. High Speed Comput..

[20]  H. Elbanna,et al.  Determination of aerodynamic sensitivity coefficients based on the three-dimensional full potential equation , 1992 .

[21]  O. Baysal,et al.  Aerodynamic shape optimization via sensitivity analysis on decomposed computational domains , 1992 .

[22]  G. Burgreen,et al.  Aerodynamic Shape Optimization Using Sensitivity Analysis on Third-Order Euler Equations , 1993 .

[23]  Oktay Baysal,et al.  Discrete aerodynamic sensitivity analysis on decomposed computational domains , 1994 .

[24]  P. A. Newman,et al.  An Approximately Factored Incremental Strategy for Calculating Consistent Discrete Aerodynamic Sensitivity Derivatives , 1992 .

[25]  G. Vanderplaats.  Approximation concepts for numerical airfoil optimization , 1979 .

[26]  Oktay Baysal,et al.  Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis , 1996 .

[27]  Meng-Sing Liou,et al.  Generalized conjugate-gradient methods for the Navier-Stokes equations , 1991 .

[28]  Bernard Grossman,et al.  Design optimization of transonic airfoils , 1993 .

[29]  D. P. Young,et al.  GMRES acceleration of computational fluid dynamics codes , 1985 .