Hydrodynamic Shape Optimization of Axisymmetric Bodies Using Multi-fidelity Modeling - Simulation and Modeling Methodologies, Technologies and Application - page 212

The algorithm of Section 4 matched the target pressure distribution (the norm of the
distributions is less than 2

10 -5 ) using less than 22 equivalent high-fidelity model
evaluations. The direct optimization of the high-fidelity model using the pattern-search
algorithm required 401 function calls to yield a comparable matching with the target.

×

Table 1. Numerical results for design Cases 1 and 2; axisymmetric hull direct drag
minimization and inverse design with a target pressure distribution, respectively. In both cases,
the flow speed is 2 m / s and the Reynolds number is 2⋅10 6 . All the numerical values are from the
high-fidelity model. N c and N f are the number of low- and high-fidelity model evaluations,
respectively. F is the norm of the difference between the target and the design shapes.

Case 1 (Drag minimization) Case 2 (Inverse design)

Variable Initial Pattern-search SBO Initial Pattern-search SBO

a 15.0000 21.8611 20.9945 18.000 24.7407 24.7667

x n 5.0000 5.6758 5.6676 7.0000 7.3704 6.8333

y n 5.0000 2.7022 2.7531 8.0000 4.7407 4.5667

x t 90.0000 98.000 96.6701 85.0000 88.1111 88.6333

y t 5.0000 0.8214 3.0290 7.0000 5.5926 5.3000

F - - - 0.0204 1.64E-5 1.93E-5

C D 0.0915 0.0853 0.0857 0.0925 0.0894 0.0893

N c - 0 300 - 0 500

N f - 282 3 - 401 5

Total cost - 282 13 - 401 < 22

Fig. 10. Case 1 results for the direct hull drag minimization, showing the initial and optimized:
(a) pressure distributions (b) skin friction distributions and (c) hull shapes; Case 2 results of the
inverse design optimization with a prescribed target pressure distribution: (d) target, initial, and
optimized pressure distributions, (e) zoom on two regions of Fig. 15(d), and (f) the initial and
optimized hull shapes