A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

IF 3.2 3区工程技术 Q2 MECHANICS

Theoretical and Applied Mechanics Letters Pub Date : 2023-09-01 DOI:10.1016/j.taml.2023.100472

Wengang Chen , Jiaqing Kou , Wenkai Yang

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Abstract

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic optimization. In this letter, the solution of unsteady adjoint equations is accelerated by dynamic mode decomposition (DMD). The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system. Thereafter, DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching. First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step. Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example, the efficiency of solving unsteady adjoint equations is significantly improved. Results show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics, and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors, which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

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基于动态模态分解的低雷诺数非定常伴随方程加速方法

在基于伴随的非定常气动优化中，非定常伴随方程的计算成本仍然很高。在这封信中，通过动态模式分解（DMD）来加速非定常伴随方程的求解。将每个实时步骤的伪时间推进近似为无限维线性动力系统。然后，利用DMD来分析从这些伪时间行进中采样的伴随向量。选择一阶零频模式来加速非定常伴随方程在每个实时步骤中的伪时间推进。通过非定常圆柱绕流和非定常气动形状优化实例，显著提高了求解非定常伴随方程的效率。结果表明，一百个伴随向量包含了足够的伪时间动力学信息，并且仅通过伴随向量产生的五个快照就可以精确地预测伴随主模，这表明非定常伴随方程伪时间推进的DMD分析是有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Applied Mechanics Letters MECHANICS-

CiteScore

6.20

自引率

2.90%

发文量

545

审稿时长

12 weeks

期刊介绍： An international journal devoted to rapid communications on novel and original research in the field of mechanics. TAML aims at publishing novel, cutting edge researches in theoretical, computational, and experimental mechanics. The journal provides fast publication of letter-sized articles and invited reviews within 3 months. We emphasize highlighting advances in science, engineering, and technology with originality and rapidity. Contributions include, but are not limited to, a variety of topics such as: • Aerospace and Aeronautical Engineering • Coastal and Ocean Engineering • Environment and Energy Engineering • Material and Structure Engineering • Biomedical Engineering • Mechanical and Transportation Engineering • Civil and Hydraulic Engineering Theoretical and Applied Mechanics Letters (TAML) was launched in 2011 and sponsored by Institute of Mechanics, Chinese Academy of Sciences (IMCAS) and The Chinese Society of Theoretical and Applied Mechanics (CSTAM). It is the official publication the Beijing International Center for Theoretical and Applied Mechanics (BICTAM).