# Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping

### Eirikur Jonsson, Leifur Leifsson, Slawomir Koziel

#### Abstract

This paper presents an efficient aerodynamic design optimization methodology for wings in transonic flow. The approach replaces the computationally expensive high-fidelity CFD model in an iterative optimization process with a corrected polynomial approximation model constructed by a cheap low-fidelity CFD model. The output space mapping technique is used to correct the approximation model to yield an accurate predictor of the high-fidelity one. Both CFD models employ the RANS equations with the Spalart-Allmaras turbulence model, but the low-fidelity one uses a coarse mesh resolution and relaxed convergence criteria. Our method is applied to a constrained lift maximization of a rectangular wing at transonic conditions with 3 design variables. The optimized designs are obtained by using 50 low-fidelity CFD model evaluations to set up the approximation model and 7 to 8 high-fidelity model evaluations, equivalent to around 10 high-fidelity CFD model evaluations.

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#### Paper Citation

#### in Harvard Style

Jonsson E., Leifsson L. and Koziel S. (2012). **Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping** . In *Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012)* ISBN 978-989-8565-20-4, pages 489-498. DOI: 10.5220/0004164004890498

#### in Bibtex Style

@conference{sddom12,

author={Eirikur Jonsson and Leifur Leifsson and Slawomir Koziel},

title={Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping},

booktitle={Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012)},

year={2012},

pages={489-498},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004164004890498},

isbn={978-989-8565-20-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012)

TI - Transonic Wing Optimization by Variable-resolution Modeling and Space Mapping

SN - 978-989-8565-20-4

AU - Jonsson E.

AU - Leifsson L.

AU - Koziel S.

PY - 2012

SP - 489

EP - 498

DO - 10.5220/0004164004890498