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Investigation of the Stability of POD-Galerkin Techniques for Reduced Order Model Development

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Technical Report,24 Nov 2015,09 Jan 2016

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AFRL/RQR Edwards AFB United States

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Detailed investigations are performed to analyze and mitigate the stability issues encountered in developing a reduced order model ROM for combustion response to specified excitations using the Euler equations. The ROM is obtained by employing Galerkins method to reduce the high-order PDEs to a lower-order ODE system by means of POD eigen-bases. Possible solutions of the ROM stability issues by changing andor by scaling the equation variables are discussed following suggestions from previous Euler equations studies. However, our evaluations using the linearized Euler equations indicate that spurious unstable modes are still encountered in the resulting ROMs. Different mean flow and boundary conditions are implemented to further evaluate the ROMs, which indicate that the presence of upstream propagating characteristic waves play an important role in affecting ROM stability. Increasing the added artificial dissipation terms is proposed and shown to be an effective method that insures that the ROMs are both numerically stable and capable of accurately reproducing the CFD solutions.

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