POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2017-01-12 DOI:10.1515/caim-2017-0011

G. Stabile, Saddam Hijazi, A. Mola, S. Lorenzi, G. Rozza

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引用次数: 96

Abstract

Abstract Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

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基于有限体积离散的POD-Galerkin降阶CFD方法:圆柱周围的涡流脱落

摘要圆柱周围的涡流脱落是一种众所周知的现象，在许多工程领域都有研究。本文提出了圆柱周围不可压缩流的降阶模型(ROM)。该ROM在较低维空间上执行控制方程的伽辽金投影。利用适当的正交分解(POD)方法生成约简基空间。重点是:(1)压力场的正确再现，在涡旋脱落现象的情况下，压力场对阻力系数和升力系数的计算是至关重要的;(ii)控制方程(动量方程和压力泊松方程)分别在速度和压力的不同简化基空间上的投影;(iii)使标准有限元POD-Galerkin方法适应有限体积框架所需的所有相关修改。根据全订单结果评估了降阶模型的准确性。

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

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.