The continuous adjoint method to the γ − R ˜ e θ t $$ \gamma -\tilde{R}{e}_{\theta t} $$ transition model coupled with the Spalart–Allmaras model for compressible flows

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Marina G. Kontou, Xenofon S. Trompoukis, Varvara G. Asouti, Kyriakos C. Giannakoglou
{"title":"The continuous adjoint method to the \n \n \n γ\n \n −\n \n \n \n R\n \n ˜\n \n \n \n e\n \n \n θ\n t\n \n \n \n $$ \\gamma -\\tilde{R}{e}_{\\theta t} $$\n transition model coupled with the Spalart–Allmaras model for compressible flows","authors":"Marina G. Kontou,&nbsp;Xenofon S. Trompoukis,&nbsp;Varvara G. Asouti,&nbsp;Kyriakos C. Giannakoglou","doi":"10.1002/fld.5319","DOIUrl":null,"url":null,"abstract":"<p>The continuous adjoint method for transitional flows of compressible fluids is developed and assessed, for the first time in the literature. The gradient of aerodynamic objective functions (aerodynamic forces) with respect to design variables, in problems governed by the compressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model and the <span></span><math>\n <semantics>\n <mrow>\n <mi>γ</mi>\n <mspace></mspace>\n <mo>−</mo>\n <mspace></mspace>\n <mover>\n <mrow>\n <mi>R</mi>\n </mrow>\n <mo>˜</mo>\n </mover>\n <msub>\n <mrow>\n <mi>e</mi>\n </mrow>\n <mrow>\n <mi>θ</mi>\n <mi>t</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$$ \\gamma -\\tilde{R}{e}_{\\theta t} $$</annotation>\n </semantics></math> transition model (in three, non-smooth and smooth, variants of it), is computed based on the continuous adjoint method. The development of the adjoint to the smooth transition model variant proved to be beneficial. The accuracy of the computed sensitivity derivatives is verified against finite differences. Programming is performed in an in-house, vertex-centered finite-volume code, efficiently running on GPUs. The proposed continuous adjoint method is used in 2D and 3D aerodynamic shape optimization problems, namely the constrained optimization of the NLF(1)–0416 isolated airfoil and that of the ONERA M6 wing. The impact of “frozen transition” (assumption according to which the adjoint to the transition model equations are not solved) or “frozen turbulence” (by additionally ignoring the adjoint to the turbulence model) are evaluated; it is shown that both lead to inaccurate sensitivities.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 11","pages":"1715-1740"},"PeriodicalIF":1.7000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5319","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Fluids","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/fld.5319","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

Abstract

The continuous adjoint method for transitional flows of compressible fluids is developed and assessed, for the first time in the literature. The gradient of aerodynamic objective functions (aerodynamic forces) with respect to design variables, in problems governed by the compressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model and the γ R ˜ e θ t $$ \gamma -\tilde{R}{e}_{\theta t} $$ transition model (in three, non-smooth and smooth, variants of it), is computed based on the continuous adjoint method. The development of the adjoint to the smooth transition model variant proved to be beneficial. The accuracy of the computed sensitivity derivatives is verified against finite differences. Programming is performed in an in-house, vertex-centered finite-volume code, efficiently running on GPUs. The proposed continuous adjoint method is used in 2D and 3D aerodynamic shape optimization problems, namely the constrained optimization of the NLF(1)–0416 isolated airfoil and that of the ONERA M6 wing. The impact of “frozen transition” (assumption according to which the adjoint to the transition model equations are not solved) or “frozen turbulence” (by additionally ignoring the adjoint to the turbulence model) are evaluated; it is shown that both lead to inaccurate sensitivities.

Abstract Image

γ-R˜eθt$$ \gamma -\tilde{R}{e}_{\theta t}$$ 过渡模型与可压缩流的 Spalart-Allmaras 模型耦合的连续邻接法
在文献中首次开发并评估了可压缩流体过渡流的连续邻接法。在可压缩 Navier-Stokes 方程与 Spalart-Allmaras 湍流模型和过渡模型(非平滑和平滑三种变体)耦合的问题中,基于连续邻接法计算了空气动力目标函数(空气动力)相对于设计变量的梯度。事实证明,开发平稳过渡模型变体的邻接法是有益的。计算出的灵敏度导数的准确性与有限差分法进行了验证。编程在内部顶点为中心的有限体积代码中进行,可在 GPU 上高效运行。提出的连续邻接法被用于二维和三维气动外形优化问题,即 NLF(1)-0416 孤立翼面和 ONERA M6 机翼的约束优化。评估了 "冻结过渡"(假设不求解过渡模型的邻接方程)或 "冻结湍流"(另外忽略湍流模型的邻接方程)的影响;结果表明,这两种情况都会导致敏感度不准确。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信