{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T14:49:16Z","timestamp":1780498156196,"version":"3.54.1"},"reference-count":44,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,20]],"date-time":"2018-01-20T00:00:00Z","timestamp":1516406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The adjoint approach in gradient-based optimization combined with computational fluid dynamics is commonly applied in various engineering fields. In this work, the gradients are used for the design of a two-dimensional airfoil shape, where the aim is a change in lift and drag coefficient, respectively, to a given target value. The optimizations use the unconstrained quasi-Newton method with an approximation of the Hessian. The flow field is computed with a finite-volume solver where the continuous adjoint approach is implemented. A common assumption in this approach is the use of the same turbulent viscosity in the adjoint diffusion term as for the primal flow field. The effect of this so-called \u201cfrozen turbulence\u201d assumption is compared to the results using adjoints to the Spalart\u2013Allmaras turbulence model. The comparison is done at a Reynolds number of     R e = 2 \u00d7  10 6      for two different airfoils at different angles of attack.<\/jats:p>","DOI":"10.3390\/computation6010005","type":"journal-article","created":{"date-parts":[[2018,1,22]],"date-time":"2018-01-22T04:51:13Z","timestamp":1516596673000},"page":"5","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Optimization of Airfoils Using the Adjoint Approach and the Influence of Adjoint Turbulent Viscosity"],"prefix":"10.3390","volume":"6","author":[{"given":"Matthias","family":"Schramm","sequence":"first","affiliation":[{"name":"ForWind, University of Oldenburg, Ammerl\u00e4nder Heerstr. 114-118, 26129 Oldenburg, Germany"},{"name":"Fraunhofer Institute for Wind Energy Systems, K\u00fcpkersweg 70, 26129 Oldenburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6626-1084","authenticated-orcid":false,"given":"Bernhard","family":"Stoevesandt","sequence":"additional","affiliation":[{"name":"Fraunhofer Institute for Wind Energy Systems, K\u00fcpkersweg 70, 26129 Oldenburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joachim","family":"Peinke","sequence":"additional","affiliation":[{"name":"ForWind, University of Oldenburg, Ammerl\u00e4nder Heerstr. 114-118, 26129 Oldenburg, Germany"},{"name":"Fraunhofer Institute for Wind Energy Systems, K\u00fcpkersweg 70, 26129 Oldenburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Arora, J.S. 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