Exploration of POD-Galerkin Techniques for Developing Reduced Order Models of the Euler Equations

Abstract

Investigations of relevant issues involved in developing a reduced order model (ROM) are performed for describing combustion response to specific excitations using Euler equations as a continued work from a previous studies using a reaction-advection scalar equation. The ROM is obtained by employing Galerkin's method to reduce the high-order PDEs to a lower-order ODE system by means of POD eigen-bases. For purposes of this study, a linearized version of the Euler equations is employed. The knowledge obtained from previous scalar equation studies is applied to ROM development of Euler equations. Numerical stability issues are encountered in Euler equation studies, the cause of which is narrowed down to normalization methods for vector variables. The effects of normalization methods are then further assessed in terms of the ROM characteristics and its predictive capability.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2015
Accession Number
ADA627047

Entities

People

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

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Advection
  • Air Force Research Laboratories
  • Chemical Reactions
  • Combustion
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Fluid Mechanics
  • Mechanical Engineering
  • Mechanics
  • Navier Stokes Equations
  • Partial Differential Equations

Fields of Study

  • Physics

Readers

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