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Computational Accuracy and Cost Method Sample Sensitivity Complex –39.049760045804646 ADIFOR –39.049760045809059 Analytic –39.049760045805281 FD –39.049724352820375 • Finite-difference is worst. • Other methods achieve the solver’s precision. Method Time Memory Complex 1.00 1.00 ADIFOR 2.33 8.09 Analytic 0.58 2.42 FD 0.88 0.72 • Analytic: best, but not easy to implement. • ADIFOR: costly. • Complex-step: good compromise. • Caveat: ratios depend on problem. – Joaquim Martins – January 12, 2000 – 13
Aerodynamic Sensitivities: FLO82 RAE 2822 Airfoil α = 3.0 o , M∞ = 0.70 Cp 1.20 0.80 0.40 0.00 -0.40 -0.80 -1.20 -1.60 -2.00 + + ++ +++++++++++++++++++++++++ + + + + + + + + + + + + + + + + + + • 2D, cell-centered, finite volume Euler solver. • Multigrid. • Implicit residual smoothing. + + + + + + + + + + + +++ + + + +++ ++++++++++++++++++++++++ • Artificial dissipation options: JST, CUSP, ECUSP and HCUSP. • Same numerical schemes as FLO87 and FLO107. – Joaquim Martins – January 12, 2000 – 14 + +++++ ++++++++++++++++++++++
Page 1 and 2: AN AUTOMATED METHOD FOR SENSITIVITY
Page 3 and 4: Sensitivity Analysis Methods • Fi
Page 5 and 6: Cauchy-Riemann Equations • Extens
Page 7 and 8: Simple Numerical Example • Estima
Page 9 and 10: Complex Functions and Operators in
Page 11 and 12: Automatic Implementation • Cookbo
Page 13: Sensitivity Estimates vs. Step Size
Page 17 and 18: Residual Convergence of Sensitivity
Page 19 and 20: Drag Coefficient Sensitivity 11 10
Page 21: Further Work • Continue to work o

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