基于有限体积离散化的CFD中Pod- galerkin降阶方法：圆柱体周围涡旋脱落
Pod-Galerkin Reduced Order Methods for CFD Using Finite Volume Discretisation: Vortex Shedding Around a Circular Cylinder
AI总结：
本文提出了一种用于不可压缩流体绕圆柱体流动的降阶模型，通过Galerkin投影在低维空间中构建，采用POD方法生成降阶基空间，重点在于准确复现压力场、在不同降阶基空间上投影动量方程和压力泊松方程，以及适应有限体积框架的必要修改，通过全阶结果验证降阶模型的准确性。
摘要：
圆柱体周围的涡旋脱落是一个广为人知且研究广泛的现象，出现在许多工程领域。本文提出了一种不可压缩流体绕圆柱体流动的降阶模型。该降阶模型是通过将支配方程投影到低维空间来构建的。降阶基空间是通过正交分解（POD）方法生成的。特别关注的是（i）压力场的正确再现，对于涡旋脱落现象，压力场对于计算阻力和升力系数至关重要；（ii）动量方程和压力泊松方程分别投影到不同的降阶基空间上；（iii）所有必要的修改，以将标准有限元POD-Galerkin方法适应到有限体积框架中。降阶模型的准确性通过全阶结果进行评估。
英文摘要：
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 flow 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 pressure 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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