Development and assessment of an intrusive polynomial chaos expansion-based continuous adjoint method for shape optimization under uncertainties,International Journal for Numerical Methods in Fluids

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Development and assessment of an intrusive polynomial chaos expansion-based continuous adjoint method for shape optimization under uncertainties
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-09-20 , DOI: 10.1002/fld.5047
A. K. Papageorgiou ₁ , E. M. Papoutsis‐Kiachagias ₁ , K. C. Giannakoglou ₁

Affiliation

This article contributes to the development of methods for shape optimization under uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos Expansion (iPCE) and continuous adjoint. The iPCE to the Navier–Stokes equations for laminar flows of incompressible fluids is developed to compute statistical moments of the Quantity of Interest which are, then, compared with those obtained through the Monte Carlo method. The optimization is carried out using a continuous adjoint-enabled, gradient-based loop. Two different formulations for the continuous adjoint to the iPCE PDEs are derived, programmed, and verified. Intrusive PCE methods for the computation of the statistical moments require mathematical development, derivation of a new system of governing equations and their numerical solution. The development is presented for a chaos order of two and two uncertain variables and can be used as a guide to those willing to extend this development to a different set of uncertain variables or chaos order. The developed method and software, programmed in OpenFOAM, is applied to two optimization problems pertaining to the flow around isolated airfoils with uncertain farfield conditions.

中文翻译：

一种基于侵入式多项式混沌展开的连续伴随法不确定条件下形状优化的开发与评估

本文基于侵入式多项式混沌展开 (iPCE) 和连续伴随法，有助于开发与流动条件相关的不确定条件下的形状优化方法。不可压缩流体层流的 iPCE 到 Navier-Stokes 方程被开发来计算感兴趣量的统计矩，然后与通过蒙特卡罗方法获得的那些进行比较。优化是使用连续伴随启用的、基于梯度的循环进行的。导出、编程和验证了 iPCE PDE 的连续伴随的两种不同公式。用于计算统计矩的侵入式 PCE 方法需要数学发展，推导新的控制方程系统及其数值解。该发展是针对两个和两个不确定变量的混沌顺序提出的，可以用作那些愿意将这种发展扩展到一组不同的不确定变量或混沌顺序的人的指南。开发的方法和软件在 OpenFOAM 中编程，应用于两个优化问题，这些问题与远场条件不确定的孤立翼型周围的流动有关。

更新日期：2021-09-20

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