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Low-dimensional POD Simulation of Unsteady Flow around Bodies with Arbitrary Shapes

Moayyedi, Mohammad Kazem | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40492 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Tayyebi Rahni, Mohammad
  7. Abstract:
  8. The aim of this research was an investigation, development, and application of low- dimensional proper orthogonal decomposition (POD) method for simulation of unsteady flow around bodies. Since analytical methods have low accuracy and limitations and also experimental methods have other problems, researchers usually use computational approaches, which mostly do not have acceptable efficiency and speeds of computations (especially in 3-D unsteady flows). On the other hand, the idea of application of reduced order modelling, which orginally comes from control theories and structural analysis, have attracted many researchers in recent years. In this research, we also used POD for reduced order modelling and the related results were applied for steady and unsteady flows. Since POD approximations have inherent errors, some parts of this work were reducing these errors.In reconstruction methods, two new approaches, namely projected and filtered POD were used to improve the accuracy of estimations. To develope low-dimensional models for unsteady flows, the governing equations were projected onto a modal space leading to the construction of a low order dynamical system. Usually, the standard reduced order models do not predict the flow time variations accurately. The accuracy of such models were improved using a calibration method. This approach is based on the combination of POD method and a least squared optimization problem. The obtained models not only predict the flow time variations accurately, but also have high speeds of computations. One of the innovations of this work is the construction of a dynamical system using static data snapshots ensemble for simulation of unsteady flow around bodies. Finally, the results obtained using POD reduced oreder models (ROM) were compared with those of direct numerical simulation (DNS) which showed adequate agreements with much lower CPU requiremnts
  9. Keywords:
  10. Numerical Simulation ; Unsteady Flow ; Reduced Order Model ; Proper Orthogonal Decomposition ; Steady Modes ; Unsteady Modes ; Calibration Strategies

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