Stability of a continuous/discrete sensitivity model for the Navier–Stokes equations

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2024-08-05 DOI:10.1002/fld.5324

N. Nouaime, B. Després, M. A. Puscas, C. Fiorini

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Abstract

This work presents a comprehensive framework for the sensitivity analysis of the Navier–Stokes equations, with an emphasis on the stability estimate of the discretized first-order sensitivity of the Navier–Stokes equations. The first-order sensitivity of the Navier–Stokes equations is defined using the polynomial chaos method, and a finite element-volume numerical scheme for the Navier–Stokes equations is suggested. This numerical method is integrated into the open-source industrial code TrioCFD developed by the CEA. The finite element-volume discretization is extended to the first-order sensitivity Navier–Stokes equations, and the most significant and original point is the discretization of the nonlinear term. A stability estimate for continuous and discrete Navier–Stokes equations is established. Finally, numerical tests are presented to evaluate the polynomial chaos method and to compare it to the Monte Carlo and Taylor expansion methods.

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纳维-斯托克斯方程连续/离散敏感性模型的稳定性

本研究提出了纳维-斯托克斯方程灵敏度分析的综合框架，重点是纳维-斯托克斯方程离散一阶灵敏度的稳定性估计。利用多项式混沌法定义了纳维-斯托克斯方程的一阶灵敏度，并提出了纳维-斯托克斯方程的有限元体积数值方案。该数值方法已集成到 CEA 开发的开源工业代码 TrioCFD 中。有限元素-体积离散化扩展到一阶敏感 Navier-Stokes 方程，最重要和最新颖的一点是非线性项的离散化。建立了连续和离散 Navier-Stokes 方程的稳定性估计。最后，通过数值测试评估了多项式混沌法，并将其与蒙特卡罗法和泰勒展开法进行了比较。

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来源期刊

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.