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

Abstract

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 and/or 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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Document Details

Document Type
Technical Report
Publication Date
Jan 09, 2016
Accession Number
AD1004930

Entities

People

  • Charles L. Merkle
  • Cheng Huang
  • Venkateswaran Sankaran
  • William E Anderson

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force Research Laboratories
  • Boundaries
  • Chemical Reactions
  • Combustion
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Dissipation
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Frequency
  • Mach Number
  • Navier Stokes Equations
  • Partial Differential Equations
  • Supersonic Flow
  • Wave Equations

Fields of Study

  • Physics

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)